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["Poisson"]
["Poisson Probability Distribution"]
["Discrete Random Variable"]
["Useful in estimating number of occurrences over a specified interval of time or space (minutes or feet/miles)"]
["Examples Random Variable:"]
["# arrivals at car wash in 1 hour"]
["# arrivals at web site in 1 hour"]
["# repairs in 5 miles of city street"]
["** Often used in waiting line situations when the random variable is # arrivals"]
[]
[]
["If two Properties are met:"]
["1) The probability of an occurrence is the same for any two intervals of equal length",null,null,null,"**link to exponetial"]
["2) The occurrence or non occurrence in any interval is independent of the occurrence or non occurrence in any other interval"]
["Then the # of occurrences is a random variable described by the Poisson Probability Distribution"]
[" "]
["Poisson Probability Function"]
["f(x) = (μxe-μ)/x!"]
["f(x)","probability of x occurrences in an interval"]
["μ = expected Value = Mean","Expected Value of Mean # of occurrences in an interval"]
["X = Random Discrete Variable","# of occurrences in interval"]
["x values = 0,1,2,3,…"]
["Mean = Variance"]
["Standard Deviation = SQRT(Mean)"]
["e",{"$f":"EXP(1)","v":2.7182818284590451},{"$f":"FTFormulaText","v":"=EXP(1)"}]
["without upper limit (but the probability is nil in the upper numbers)"]
["When calculating Prob. For different time interval, you must convert the mean arrival rate to the time period: (New Time)/(Old Time)*Mean or (New Length)/(Old Length)*Mean ==> Part/Whole*Mean"]
[]
["Example 1"]
["# arrivals at drive up bank window"]
["assume 1: probability of a car arriving in the same for any two time periods of equal length"]
["assume 1: prob of car arriving is same for any two equal length time periods"]
["assume 2: arrival or nonarrival of a car in any time period is independent of the arrival or nonarrival in any other time period"]
["Assume 2: arrival or nonarrival in 1 time period is independent of arrival or nonarrival in any other period"]
[]
["Time interval",15,"minutes",null,"x",0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30]
["Mean arrival",10,"cars",null,"P(x)",{"$f":"_xlfn.POISSON.DIST(F36,$B$37,0)","v":4.5399929762484854E-5},{"$f":"_xlfn.POISSON.DIST(G36,$B$37,0)","v":4.5399929762484861E-4},2.2699964881242444E-3,7.5666549604141483E-3,1.8916637401035354E-2,3.7833274802070715E-2,6.3055458003451192E-2,9.0079225719215977E-2,0.11259903214901996,0.1251100357211333,0.1251100357211333,0.11373639611012118,9.4780330091767673E-2,7.2907946224436637E-2,5.2077104446026187E-2,3.4718069630684127E-2,2.1698793519177549E-2,1.2763996187751522E-2,7.0911089931952852E-3,3.7321626279975249E-3,1.8660813139987594E-3,8.8861014952321864E-4,4.0391370432873514E-4,1.7561465405597289E-4,7.317277252332188E-5,2.926910900932863E-5,1.1257349618972562E-5,4.1693887477676179E-6,1.4890674099170117E-6,5.1347152066103749E-7,1.7115717355367883E-7]
["Random Variable =",{"$f":"\"# arrivals in \"&B36&\" minutes\"&CHAR(10)&\"(Mean = \"&B37&\" \"&C37&\")\"","v":"# arrivals in 15 minutes\n(Mean = 10 cars)"},"."]
["x",5]
["f(x) = (μxe-μ)/x!"]
[{"$f":"\"P(x=\"&$B$39&\")\"","v":"P(x=5)"},{"$f":"($B$37^B39*EXP(1)^-$B$37)/FACT(B39)","v":3.7833274802070729E-2}]
[{"$f":"\"P(x=\"&$B$39&\")\"","v":"P(x=5)"},{"$f":"_xlfn.POISSON.DIST(B39,$B$37,0)","v":3.7833274802070715E-2},"with discrete probability functions 0 = probability = height of column"]
["Example 2"]
["Time interval",3,"minutes"]
[{"$f":"\"Mean arrival = \"&B44&\"/\"&B36&\"*\"&B37&\" =\"","v":"Mean arrival = 3/15*10 ="},{"$f":"B44/B36*B37","v":2},"cars","New Mean = (New Time)/(Old Time)*Mean"]
["Random Variable =",{"$f":"\"# arrivals in \"&B44&\" minutes\"&CHAR(10)&\"(Mean = \"&B45&\" \"&C45&\")\"","v":"# arrivals in 3 minutes\n(Mean = 2 cars)"}]
["x",1,null,null,"x",0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30]
["f(x) = (μxe-μ)/x!",null,null,null,"P(x)",{"$f":"_xlfn.POISSON.DIST(F47,$B$45,0)","v":0.1353352832366127},{"$f":"_xlfn.POISSON.DIST(G47,$B$45,0)","v":0.27067056647322535},0.27067056647322546,0.18044704431548364,9.022352215774182E-2,3.6089408863096716E-2,1.2029802954365572E-2,3.4370865583901629E-3,8.5927163959754148E-4,1.9094925324389769E-4,3.8189850648779602E-5,6.9436092088690095E-6,1.1572682014781686E-6,1.7804126176587265E-7,2.5434465966553194E-8,3.391262128873753E-9,4.2390776610922124E-10,4.9871501895202335E-11,5.5412779883558056E-12,5.8329241982692627E-13,5.8329241982692291E-14,5.5551659031135841E-15,5.0501508210123689E-16,4.3914354965324941E-17,3.6595295804437333E-18,2.9276236643549582E-19,2.2520182033499883E-20,1.6681616321111046E-21,1.1915440229365106E-22,8.21754498576894E-24,5.4783633238460017E-25]
[{"$f":"\"P(x=\"&$B$47&\")\"","v":"P(x=1)"},{"$f":"(B45^B47*EXP(1)^-B45)/FACT(B47)","v":0.2706705664732254}]
[{"$f":"\"P(x=\"&$B$47&\")\"","v":"P(x=1)"},{"$f":"_xlfn.POISSON.DIST(B47,B45,0)","v":0.27067056647322535}]
["Example 3"]
["# defects in road"]
["assume 1: prob of a defect is the same for any 2 highway intervals of equal length"]
["assume 2: occurrence or nonoccurrence of defects for any 1 interval is independent of the occurrence or nonoccurrence in any other interval"]
["Interval = Length =",1,"mile"]
["Mean =",2,"defects"]
["Random Variable =",{"$f":"\"# defects in \"&B55&\" \"&C55&\" stretch\"","v":"# defects in 1 mile stretch"}]
["Interval = Length =",3,"miles"]
["Mean =",{"$f":"B58/B55*B56","v":6},"defects","New Mean = (New Length)/(Old Length)*Mean"]
["Random Variable =",{"$f":"\"# defects in \"&B58&\" \"&C58&\" stretch\"&CHAR(10)&\"(Mean = \"&B59&\" \"&C59&\")\"","v":"# defects in 3 miles stretch\n(Mean = 6 defects)"},"."]
["x",0,null,null,null,"x",0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30]
[{"$f":"\"P(x=\"&$B$61&\")\"","v":"P(x=0)"},{"$f":"B59^B61*EXP(1)^-B59","v":2.4787521766663594E-3},{"$f":"\"P(of \"&B61&\" defects in \"&$B$58&\" \"&$C$58&\")\"","v":"P(of 0 defects in 3 miles)"},null,null,"P(x)",{"$f":"_xlfn.POISSON.DIST(G61,$B$59,0)","v":2.4787521766663585E-3},{"$f":"_xlfn.POISSON.DIST(H61,$B$59,0)","v":1.4872513059998151E-2},4.4617539179994462E-2,8.9235078359988909E-2,0.13385261753998337,0.16062314104798003,0.16062314104798003,0.13767697804112577,0.10325773353084432,6.883848902056286E-2,4.1303093412337732E-2,2.2528960043093311E-2,1.1264480021546661E-2,5.1989907791753836E-3,2.2281389053608732E-3,8.9125556214435036E-4,3.3422083580413167E-4,1.1796029498969329E-4,3.9320098329897816E-5,1.241687315680987E-5,3.725061947042944E-6,1.0643034134408412E-6,2.9026456730204751E-7,7.5721191470099433E-8,1.8930297867524921E-8,4.543271488205959E-9,1.0484472665090706E-9,2.329882814464599E-10,4.99260603099557E-11,1.0329529719301251E-11,2.0659059438602391E-12]
[{"$f":"\"P(x=\"&$B$61&\")\"","v":"P(x=0)"},{"$f":"_xlfn.POISSON.DIST(B61,B59,0)","v":2.4787521766663585E-3}]
["x",1]
[{"$f":"\"P(at least \"&$B$64&\")\"","v":"P(at least 1)"},{"$f":"1-B62","v":0.99752124782333362},{"$f":"\"P(of at least \"&B64&\" defects in \"&$B$58&\" \"&$C$58&\")\"","v":"P(of at least 1 defects in 3 miles)"}]
[{"$f":"\"P(at least \"&$B$64&\")\"","v":"P(at least 1)"},{"$f":"1-_xlfn.POISSON.DIST(B64-1,B59,1)","v":0.99752124782333362}]
[]
["Problem 61 chapter 5"]
["Cars arrive randomly and independently"]
["Probability of an arrival is the same for any two  time intervals of equal length "]
["Time Period =",1,"hour","in"]
["Mean",15,"cars"]
["Thing counted","arrivals",null,"x",0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54]
["Random Variable",{"$f":"\"# of \"&B73&\" \"&D71&\" \"&B71&\" \"&C71","v":"# of arrivals in 1 hour"},null,"P(x)",{"$f":"_xlfn.POISSON.DIST(E73,$B$72,0)","v":3.0590232050182579E-7},{"$f":"_xlfn.POISSON.DIST(F73,$B$72,0)","v":4.5885348075273872E-6},3.4414011056455447E-5,1.7207005528227688E-4,6.4526270730853874E-4,1.9357881219256175E-3,4.839470304814038E-3,1.0370293510315797E-2,1.9444300331842138E-2,3.2407167219736882E-2,4.8610750829605344E-2,6.6287387494916333E-2,8.2859234368645451E-2,9.5606808886898584E-2,0.10243586666453419,0.10243586666453419,9.6033624998000819E-2,8.4735551468824222E-2,7.0612959557353555E-2,5.5747073334752775E-2,4.1810305001064599E-2,2.9864503572189009E-2,2.0362161526492496E-2,1.3279670560755973E-2,8.2997941004724716E-3,4.9798764602834869E-3,2.8730056501635559E-3,1.5961142500908597E-3,8.5506120540581904E-4,4.4227303727887191E-4,2.2113651863943614E-4,{"$f":"_xlfn.POISSON.DIST(AJ73,$B$72,0)","v":1.0700154127714583E-4},{"$f":"_xlfn.POISSON.DIST(AK73,$B$72,0)","v":5.0156972473662407E-5},{"$f":"_xlfn.POISSON.DIST(AL73,$B$72,0)","v":2.2798623851664678E-5},{"$f":"_xlfn.POISSON.DIST(AM73,$B$72,0)","v":1.0058216405146199E-5},{"$f":"_xlfn.POISSON.DIST(AN73,$B$72,0)","v":4.3106641736340825E-6},{"$f":"_xlfn.POISSON.DIST(AO73,$B$72,0)","v":1.7961100723475384E-6},{"$f":"_xlfn.POISSON.DIST(AP73,$B$72,0)","v":7.2815273203278476E-7},{"$f":"_xlfn.POISSON.DIST(AQ73,$B$72,0)","v":2.8742871001294135E-7},{"$f":"_xlfn.POISSON.DIST(AR73,$B$72,0)","v":1.105495038511311E-7},{"$f":"_xlfn.POISSON.DIST(AS73,$B$72,0)","v":4.1456063944174359E-8},{"$f":"_xlfn.POISSON.DIST(AT73,$B$72,0)","v":1.5166852662502828E-8},{"$f":"_xlfn.POISSON.DIST(AU73,$B$72,0)","v":5.416733093751035E-9},{"$f":"_xlfn.POISSON.DIST(AV73,$B$72,0)","v":1.8895580559596564E-9},{"$f":"_xlfn.POISSON.DIST(AW73,$B$72,0)","v":6.4416751907715665E-10},{"$f":"_xlfn.POISSON.DIST(AX73,$B$72,0)","v":2.1472250635905038E-10},{"$f":"_xlfn.POISSON.DIST(AY73,$B$72,0)","v":7.0018208595342535E-11},{"$f":"_xlfn.POISSON.DIST(AZ73,$B$72,0)","v":2.234623678574756E-11},{"$f":"_xlfn.POISSON.DIST(BA73,$B$72,0)","v":6.9831989955461589E-12},{"$f":"_xlfn.POISSON.DIST(BB73,$B$72,0)","v":2.1377139782284068E-12},{"$f":"_xlfn.POISSON.DIST(BC73,$B$72,0)","v":6.4131419346851647E-13},{"$f":"_xlfn.POISSON.DIST(BD73,$B$72,0)","v":1.8862182160838988E-13},{"$f":"_xlfn.POISSON.DIST(BE73,$B$72,0)","v":5.4410140848574323E-14},{"$f":"_xlfn.POISSON.DIST(BF73,$B$72,0)","v":1.5399096466577602E-14},{"$f":"_xlfn.POISSON.DIST(BG73,$B$72,0)","v":4.2775267962715488E-15}]
["x",20]
["Operator",">=",null,"check"]
[{"$f":"\"P(x\"&B76&B75&\") =\"","v":"P(x>=20) ="},{"$f":"1-_xlfn.POISSON.DIST(B75-1,B72,1)","v":0.12478121503252482},null,{"$f":"SUM(Y74:BG74)","v":0.12478121503252329}]
[{"$f":"\"P(x\"&B76&B75&\") =\"","v":"P(x>=20) ="}]
[]
["Problem 62 chapter 5"]
["# break downs per day are random and independent"]
["Probability of a break down is the same for any two  time intervals of equal length "]
["Time Period =",1,"day","in"]
["Mean",1.5,"break downs"]
["Thing counted",{"$f":"C84","v":"break downs"}]
["Random Variable",{"$f":"\"# of \"&B85&\" \"&D83&\" \"&B83&\" \"&C83","v":"# of break downs in 1 day"},null,"x",0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23]
["x",3,null,"P(x)",{"$f":"_xlfn.POISSON.DIST(E86,$B$84,0)","v":0.22313016014842982},{"$f":"_xlfn.POISSON.DIST(F86,$B$84,0)","v":0.33469524022264474},0.25102143016698358,0.12551071508349182,4.7066518156309439E-2,1.4119955446892818E-2,3.5299888617232088E-3,7.5642618465497267E-4,1.4182990962280739E-4,2.3638318270467916E-5,3.5457477405701846E-6,4.8351105553229772E-7,6.0438881941537506E-8,6.9737171471004864E-9,7.4718398004647881E-10,7.471839800464716E-11,7.0048498129357136E-12,6.1807498349433059E-13,5.1506248624527156E-14,4.0662827861468805E-15,3.0497120896101673E-16,2.1783657782929996E-17,1.4852493942906728E-18,9.6864090931999799E-20]
["Operator",">="]
[{"$f":"\"P(x\"&B88&B87&\") =\"","v":"P(x>=3) ="},{"$f":"1-_xlfn.POISSON.DIST(B87-1,B84,1)","v":0.19115316946194194}]
[{"$f":"\"P(x\"&B88&B87&\") =\"","v":"P(x>=3) ="}]
[]
["Problem 40 chapter 5"]
["Time Interval",1,"hour"]
["mean",48,"calls"]
["New Time",5,"minutes",null,null,null,"x",0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23]
["New Time",{"$f":"B95/60","v":8.3333333333333329E-2},"hour",null,null,null,"P(x)",{"$f":"_xlfn.POISSON.DIST(H95,$B$97,0)","v":1.8315638888734179E-2},{"$f":"_xlfn.POISSON.DIST(I95,$B$97,0)","v":7.3262555554936715E-2},0.14652511110987346,0.19536681481316462,0.19536681481316462,0.1562934518505317,0.10419563456702115,5.9540362609726373E-2,2.9770181304863183E-2,1.3231191691050297E-2,5.2924766764201169E-3,1.9245369732436813E-3,6.4151232441456022E-4,1.9738840751217212E-4,5.6396687860620615E-5,1.5039116762832177E-5,3.7597791907080502E-6,8.8465392722542387E-7,1.9658976160564875E-7,4.1387318232768188E-8,8.2774636465536645E-9,1.5766597422006992E-9,2.8666540767285399E-10,4.9854853508322518E-11]
["New Mean",{"$f":"B96/B93*B94","v":4},"New Mean = (New Time)/(Old Time)*Mean"]
["x",3,null,"check"]
[{"$f":"\"P(x=\"&B98&\" \"&C94&\" in \"&B95&\" \"&C95&\")\"","v":"P(x=3 calls in 5 minutes)"},{"$f":"_xlfn.POISSON.DIST(B98,B97,0)","v":0.19536681481316462},null,{"$f":"K96","v":0.19536681481316462}]
[]
["New Time",15,"minutes",null,null,null,"x",0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23]
["New Time",{"$f":"B101/60","v":0.25},"hour",null,null,null,"P(x)",{"$f":"_xlfn.POISSON.DIST(H101,$B$103,0)","v":6.1442123533282098E-6},{"$f":"_xlfn.POISSON.DIST(I101,$B$103,0)","v":7.3730548239938514E-5},4.423832894396313E-4,1.7695331577585235E-3,5.3085994732755765E-3,1.2740638735861376E-2,2.5481277471722744E-2,4.3682189951524682E-2,6.5523284927287068E-2,8.7364379903049433E-2,0.10483725588365932,0.11436791550944653,0.11436791550944654,0.10557038354718144,9.0488900183298387E-2,7.2391120146638691E-2,5.4293340109979028E-2,3.8324710665867553E-2,2.5549807110578349E-2,1.6136720280365273E-2,9.6820321682191679E-3,5.5325898104109563E-3,3.0177762602241584E-3,1.5744919618560791E-3]
["New Mean",{"$f":"B102/B93*B94","v":12},"New Mean = (New Time)/(Old Time)*Mean"]
["x",10,null,"check"]
[{"$f":"\"P(x=\"&B104&\" \"&C100&\" in \"&B101&\" \"&C101&\")\"","v":"P(x=10  in 15 minutes)"},{"$f":"_xlfn.POISSON.DIST(B104,B103,0)","v":0.10483725588365932},null,{"$f":"R102","v":0.10483725588365932}]
[]
[]
["New Time",5,"minutes",null,null,null,"x",0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23]
["New Time",{"$f":"B108/60","v":8.3333333333333329E-2},"hour",null,null,null,"P(x)",{"$f":"_xlfn.POISSON.DIST(H108,$B$110,0)","v":1.8315638888734179E-2},{"$f":"_xlfn.POISSON.DIST(I108,$B$110,0)","v":7.3262555554936715E-2},0.14652511110987346,0.19536681481316462,0.19536681481316462,0.1562934518505317,0.10419563456702115,5.9540362609726373E-2,2.9770181304863183E-2,1.3231191691050297E-2,5.2924766764201169E-3,1.9245369732436813E-3,6.4151232441456022E-4,1.9738840751217212E-4,5.6396687860620615E-5,1.5039116762832177E-5,3.7597791907080502E-6,8.8465392722542387E-7,1.9658976160564875E-7,4.1387318232768188E-8,8.2774636465536645E-9,1.5766597422006992E-9,2.8666540767285399E-10,4.9854853508322518E-11]
["New Mean",{"$f":"B109/B93*B94","v":4},"New Mean = (New Time)/(Old Time)*Mean"]
["Expected Mean =",{"$f":"B110","v":4}]
[]
["New Time",3,"minutes"]
["New Time Hours",{"$f":"B113/60","v":0.05},"hours",null,"x",0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23]
["New Mean",{"$f":"B114/B93*B94","v":2.4000000000000004},null,null,"P(x)",{"$f":"_xlfn.POISSON.DIST(F114,$B$115,0)","v":9.071795328941247E-2},{"$f":"_xlfn.POISSON.DIST(G114,$B$115,0)","v":0.21772308789458997},0.26126770547350803,0.20901416437880643,0.12540849862728387,6.0196079341096276E-2,2.4078431736438529E-2,8.2554623096360684E-3,2.4766386928908187E-3,6.6043698477088488E-4,1.5850487634501241E-4,3.4582882111638978E-5,6.916576422327824E-6,1.2769064164297519E-6,2.188982428165286E-7,3.5023718850644576E-8,5.2535578275966965E-9,7.4167875213130393E-10,9.8890500284173374E-11,1.2491431614842898E-11,1.4989717937811447E-12,1.7131106214641822E-13,1.8688479506881864E-14,1.9501022094137532E-15]
["x",0]
[{"$f":"\"P(x=\"&B116&\" \"&$C$94&\" in \"&B113&\" \"&C113&\")\"","v":"P(x=0 calls in 3 minutes)"},{"$f":"_xlfn.POISSON.DIST(B116,B115,0)","v":9.071795328941247E-2}]

{"sheet":"EX","index":1,"n_rows":48,"n_cols":379,"rows_kept":48,"cut":false,"hidden":false,"merged":[]}
[null,"Exponential"]
[null,"Exponential Probability Distribution"]
[null,"Continuous Random Variable"]
[null,"Useful in computing probabilities for the time it takes to complete a task"]
[null,"Useful in computing probability for the length (time or space - (minutes or feet/miles)) between occurrences (1 car arrival & next car arrival, start loading truck & end loading truck, defect 1 in highway & next defect)"]
[null,"Examples Random Variable:"]
[null,"Time between arrivals at car wash"]
[null,"Time required to load truck"]
[null,"Distance between major defects in a highway"]
[]
[null,"Exponential Probability Functions (2 one density (height) and one cumulative probabilities)"]
[1,"f(x) = (1/μ)*e-x/μ","For x >=0","Density Function to determine Height or curve, not probability"]
[2,"P(x<=x0) = 1- e-x0/μ","Used to calculate Cumulative"]
[null,"F(x)","Probability of length of interval (time or space)"]
[null,"Continuous Random Variable = x =","Length of interval (time or space - minutes/hours or feet/miles)"]
[null,"Mean = Expected Value = μ"]
[null,"e = =EXP(1)",{"$f":"EXP(1)","v":2.7182818284590451}]
[null,"without upper limit (but the probability is nil in the upper numbers)"]
[null,"Mean = Standard Deviation"]
[]
[null,"Example 1"]
[null,{"$f":"\"Time To Load Truck, mew = \"&C23&\" \"&D23","v":"Time To Load Truck, mew = 15 Minutes"},null,null,null,{"$f":"B30&\" = \"&ROUND(C30,4)","v":"P(0 <= Minutes To Load Truck <= 6) = 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23,0)","v":4.9643887139495585E-4},{"$f":"_xlfn.EXPON.DIST(EY23,1/$C$23,0)","v":4.8016366931831727E-4},{"$f":"_xlfn.EXPON.DIST(EZ23,1/$C$23,0)","v":4.6442203183119424E-4},{"$f":"_xlfn.EXPON.DIST(FA23,1/$C$23,0)","v":4.4919646660569778E-4},{"$f":"_xlfn.EXPON.DIST(FB23,1/$C$23,0)","v":4.3447005478065864E-4},{"$f":"_xlfn.EXPON.DIST(FC23,1/$C$23,0)","v":4.2022643216115224E-4},{"$f":"_xlfn.EXPON.DIST(FD23,1/$C$23,0)","v":4.0644977103437586E-4},{"$f":"_xlfn.EXPON.DIST(FE23,1/$C$23,0)","v":3.9312476258167322E-4},{"$f":"_xlfn.EXPON.DIST(FF23,1/$C$23,0)","v":3.8023659986716012E-4},{"$f":"_xlfn.EXPON.DIST(FG23,1/$C$23,0)","v":3.6777096138405143E-4},{"$f":"_xlfn.EXPON.DIST(FH23,1/$C$23,0)","v":3.557139951404006E-4},{"$f":"_xlfn.EXPON.DIST(FI23,1/$C$23,0)","v":3.4405230326657355E-4},{"$f":"_xlfn.EXPON.DIST(FJ23,1/$C$23,0)","v":3.3277292712734777E-4},{"$f":"_xlfn.EXPON.DIST(FK23,1/$C$23,0)","v":3.2186333292209606E-4},{"$f":"_xlfn.EXPON.DIST(FL23,1/$C$23,0)","v":3.1131139775705146E-4},{"$f":"_xlfn.EXPON.DIST(FM23,1/$C$23,0)","v":3.0110539617417774E-4},{"$f":"_xlfn.EXPON.DIST(FN23,1/$C$23,0)","v":2.9123398712167775E-4},{"$f":"_xlfn.EXPON.DIST(FO23,1/$C$23,0)","v":2.816862013516559E-4},{"$f":"_xlfn.EXPON.DIST(FP23,1/$C$23,0)","v":2.7245142923093779E-4},{"$f":"_xlfn.EXPON.DIST(FQ23,1/$C$23,0)","v":2.6351940895149689E-4},{"$f":"_xlfn.EXPON.DIST(FR23,1/$C$23,0)","v":2.5488021512738983E-4},{"$f":"_xlfn.EXPON.DIST(FS23,1/$C$23,0)","v":2.4652424776552882E-4},{"$f":"_xlfn.EXPON.DIST(FT23,1/$C$23,0)","v":2.3844222159803466E-4},{"$f":"_xlfn.EXPON.DIST(FU23,1/$C$23,0)","v":2.3062515576431722E-4},{"$f":"_xlfn.EXPON.DIST(FV23,1/$C$23,0)","v":2.2306436383141812E-4},{"$f":"_xlfn.EXPON.DIST(FW23,1/$C$23,0)","v":2.1575144414152366E-4},{"$f":"_xlfn.EXPON.DIST(FX23,1/$C$23,0)","v":2.0867827047592587E-4},{"$f":"_xlfn.EXPON.DIST(FY23,1/$C$23,0)","v":2.0183698302505434E-4},{"$f":"_xlfn.EXPON.DIST(FZ23,1/$C$23,0)","v":1.9521997965454591E-4},{"$f":"_xlfn.EXPON.DIST(GA23,1/$C$23,0)","v":1.8881990745764647E-4},{"$f":"_xlfn.EXPON.DIST(GB23,1/$C$23,0)","v":1.8262965458455788E-4},{"$f":"_xlfn.EXPON.DIST(GC23,1/$C$23,0)","v":1.7664234233965179E-4},{"$f":"_xlfn.EXPON.DIST(GD23,1/$C$23,0)","v":1.7085131753776555E-4},{"$f":"_xlfn.EXPON.DIST(GE23,1/$C$23,0)","v":1.6525014511109058E-4},{"$f":"_xlfn.EXPON.DIST(GF23,1/$C$23,0)","v":1.5983260095843462E-4},{"$f":"_xlfn.EXPON.DIST(GG23,1/$C$23,0)","v":1.5459266502891369E-4},{"$f":"_xlfn.EXPON.DIST(GH23,1/$C$23,0)","v":1.4952451463238689E-4},{"$f":"_xlfn.EXPON.DIST(GI23,1/$C$23,0)","v":1.4462251796920188E-4},{"$f":"_xlfn.EXPON.DIST(GJ23,1/$C$23,0)","v":1.3988122787206018E-4},{"$f":"_xlfn.EXPON.DIST(GK23,1/$C$23,0)","v":1.3529537575304894E-4},{"$f":"_xlfn.EXPON.DIST(GL23,1/$C$23,0)","v":1.3085986574911174E-4},{"$f":"_xlfn.EXPON.DIST(GM23,1/$C$23,0)","v":1.2656976905945467E-4},{"$f":"_xlfn.EXPON.DIST(GN23,1/$C$23,0)","v":1.2242031846859382E-4},{"$f":"_xlfn.EXPON.DIST(GO23,1/$C$23,0)","v":1.1840690304895861E-4},{"$f":"_xlfn.EXPON.DIST(GP23,1/$C$23,0)","v":1.145250630371647E-4},{"$f":"_xlfn.EXPON.DIST(GQ23,1/$C$23,0)","v":1.1077048487826225E-4},{"$f":"_xlfn.EXPON.DIST(GR23,1/$C$23,0)","v":1.0713899643245383E-4},{"$f":"_xlfn.EXPON.DIST(GS23,1/$C$23,0)","v":1.0362656233895355E-4},{"$f":"_xlfn.EXPON.DIST(GT23,1/$C$23,0)","v":1.0022927953183815E-4},{"$f":"_xlfn.EXPON.DIST(GU23,1/$C$23,0)","v":9.6943372902905437E-5},{"$f":"_xlfn.EXPON.DIST(GV23,1/$C$23,0)","v":9.3765191106721181E-5},{"$f":"_xlfn.EXPON.DIST(GW23,1/$C$23,0)","v":9.0691202503192928E-5},{"$f":"_xlfn.EXPON.DIST(GX23,1/$C$23,0)","v":8.7717991233162202E-5},{"$f":"_xlfn.EXPON.DIST(GY23,1/$C$23,0)","v":8.4842253422653859E-5},{"$f":"_xlfn.EXPON.DIST(GZ23,1/$C$23,0)","v":8.2060793511565399E-5},{"$f":"_xlfn.EXPON.DIST(HA23,1/$C$23,0)","v":7.9370520702715382E-5},{"$f":"_xlfn.EXPON.DIST(HB23,1/$C$23,0)","v":7.6768445527306705E-5},{"$f":"_xlfn.EXPON.DIST(HC23,1/$C$23,0)","v":7.4251676522986887E-5},{"$f":"_xlfn.EXPON.DIST(HD23,1/$C$23,0)","v":7.1817417020814684E-5},{"$f":"_xlfn.EXPON.DIST(HE23,1/$C$23,0)","v":6.9462962037562426E-5},{"$f":"_xlfn.EXPON.DIST(HF23,1/$C$23,0)","v":6.7185695269900749E-5},{"$f":"_xlfn.EXPON.DIST(HG23,1/$C$23,0)","v":6.4983086187125698E-5},{"$f":"_xlfn.EXPON.DIST(HH23,1/$C$23,0)","v":6.2852687219197836E-5},{"$f":"_xlfn.EXPON.DIST(HI23,1/$C$23,0)","v":6.0792131036967752E-5},{"$f":"_xlfn.EXPON.DIST(HJ23,1/$C$23,0)","v":5.8799127921567067E-5},{"$f":"_xlfn.EXPON.DIST(HK23,1/$C$23,0)","v":5.6871463220040747E-5},{"$f":"_xlfn.EXPON.DIST(HL23,1/$C$23,0)","v":5.500699488439364E-5},{"$f":"_xlfn.EXPON.DIST(HM23,1/$C$23,0)","v":5.3203651091316866E-5},{"$f":"_xlfn.EXPON.DIST(HN23,1/$C$23,0)","v":5.1459427939948678E-5},{"$f":"_xlfn.EXPON.DIST(HO23,1/$C$23,0)","v":4.9772387225111944E-5},{"$f":"_xlfn.EXPON.DIST(HP23,1/$C$23,0)","v":4.8140654283553196E-5},{"$f":"_xlfn.EXPON.DIST(HQ23,1/$C$23,0)","v":4.6562415910790697E-5},{"$f":"_xlfn.EXPON.DIST(HR23,1/$C$23,0)","v":4.5035918346256291E-5},{"$f":"_xlfn.EXPON.DIST(HS23,1/$C$23,0)","v":4.355946532449204E-5},{"$f":"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[null,"mew = expected loading time for truck",15,"Minutes",null,"x",0,{"$f":"G23+0.5","v":0.5},{"$f":"H23+0.5","v":1},1.5,2,2.5,3,3.5,4,4.5,5,5.5,6,6.5,7,7.5,8,8.5,9,9.5,10,10.5,11,11.5,12,12.5,13,13.5,14,14.5,15,15.5,16,16.5,17,17.5,18,18.5,19,19.5,20,20.5,21,21.5,22,22.5,23,23.5,24,24.5,25,25.5,26,26.5,27,27.5,28,28.5,29,29.5,{"$f":"BN23+0.5","v":30},30.5,31,31.5,32,32.5,33,33.5,34,34.5,35,35.5,36,36.5,37,37.5,38,38.5,39,39.5,40,40.5,41,41.5,42,42.5,43,43.5,44,44.5,45,45.5,46,46.5,47,47.5,48,48.5,49,49.5,50,50.5,51,51.5,52,52.5,53,53.5,54,54.5,55,55.5,56,56.5,57,57.5,58,58.5,59,59.5,60,60.5,61,61.5,{"$f":"DZ23+0.5","v":62},62.5,63,63.5,64,64.5,65,65.5,66,66.5,67,67.5,68,68.5,69,69.5,70,70.5,71,71.5,72,72.5,73,73.5,74,{"$f":"EY23+0.5","v":74.5},{"$f":"EZ23+0.5","v":75},75.5,76,76.5,77,77.5,78,78.5,79,79.5,80,80.5,81,81.5,82,82.5,83,83.5,84,84.5,85,85.5,86,86.5,87,87.5,88,88.5,89,89.5,90,90.5,91,91.5,92,92.5,93,93.5,94,94.5,95,95.5,96,96.5,97,97.5,98,98.5,99,99.5,100,100.5,101,101.5,102,102.5,103,103.5,104,104.5,105,105.5,106,106.5,{"$f":"HL23+0.5","v":107},107.5,108,108.5,109,109.5,110,110.5,111,111.5,112,112.5,113,113.5,114,114.5,115,115.5,116,116.5,117,117.5,118,118.5,119,119.5,120,120.5,121,121.5,122,122.5,123,123.5,124,124.5,125,125.5,126,126.5,127]
[null,"Random Continuous Variable = x = Time To Load Truck",null,null,null,{"$f":"B32&\" = \"&ROUND(C33,4)","v":"P(6 <= Minutes To Load Truck <= 18) = 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[null,"X min",0]
[null,"x1",6]
[null,"x2",18]
[null,"x3",25]
[null,{"$f":"\"P(\"&C26&\" <= \"&$C$25&\" <= \"&C27&\")\"","v":"P(0 <= Minutes To Load Truck <= 6)"},{"$f":"1-EXP(1)^-(C27/C23)","v":0.32967995396436067}]
[null,{"$f":"B30","v":"P(0 <= Minutes To Load Truck <= 6)"},{"$f":"_xlfn.EXPON.DIST(C27,1/C23,1)","v":0.32967995396436073}]
[null,{"$f":"\"P(\"&C27&\" <= \"&$C$25&\" <= \"&C28&\")\"","v":"P(6 <= Minutes To Load Truck <= 18)"},{"$f":"(1-EXP(1)^-(C28/C23))-(1-EXP(1)^-(C27/C23))","v":0.36912583412343714}]
[null,{"$f":"B32","v":"P(6 <= Minutes To Load Truck <= 18)"},{"$f":"_xlfn.EXPON.DIST(C28,1/C23,1)-_xlfn.EXPON.DIST(C27,1/C23,1)","v":0.36912583412343708}]
[null,{"$f":"\"P(\"&$C$25&\" >= \"&C29&\")\"","v":"P(Minutes To Load Truck >= 25)"},{"$f":"1-_xlfn.EXPON.DIST(C29,1/C23,1)","v":0.18887560283756177}]
[null,{"$f":"B34","v":"P(Minutes To Load Truck >= 25)"},{"$f":"EXP(1)^-(C29/C23)","v":0.18887560283756183}]
[]
[null,"Problem 46 chapter 6"]
[null,"Time (minutes) between phone calls at Insurance Claims Office Follows Exponential Distribution"]
[null,{"$f":"\"x = time between phone calls in \"&D41","v":"x = time between phone calls in minutes"},"minutes"]
[null,"1/μ =",0.5,null,null,"check",{"$f":"1/C41*EXP(1)^-(G42/C41)","v":0.5}]
[null,"Mew = Expected Mean 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[null,"x1",0.5]
[null,"x2",1]
[null,"x3",5]
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{"sheet":"P&E","index":2,"n_rows":51,"n_cols":68,"rows_kept":51,"cut":false,"hidden":false,"merged":[]}
["Poisson","POISSON.DIST"]
["Discrete Random Variable"]
["# of occurrences in an interval (time or space)"]
["f(x) = (μxe-μ)/x!","Height & Probability"]
["f(x)","probability of x occurrences in an interval"]
["X = Random Discrete Variable","# of occurrences in interval"]
["μ = Expected Value = Mean =","Expected Value of Mean = # of occurrences in an interval"]
["x values = 0,1,2,3,…"]
["without upper limit (but the probability is nil in the upper numbers)"]
["Mean = Variance"]
[]
["Exponential","EXPON.DIST"]
["Continuous Random Variable"]
["Probability of length of interval (time or space) between occurrences"]
["f(x) = (1/μ)*e-x/μ        For x >=0","Density Function to determine Height of curve, not probability"]
["P(x<=x0) = 1- e-x0/μ","Used to calculate cumulative"]
["P(x)","Probability of length of interval (time or space)"]
["X = Continuous Random Variable","Length of interval between two occurrences  (time or space - minutes/hours or feet/miles)"]
["μ = Mean = Expected Value =","Expected Value of Mean = time between occurrences (1 arrival and next or beg and end)"]
["x values > = 0"]
["without upper limit (but the probability is nil in the upper numbers)"]
["Mean = Standard Deviation"]
[]
["If Poisson Distribution describes # of occurrences in an internal, then the Exponential Distribution describes length of interval (probability of)",null,null,null,null,null,null,null,null,"Falses are disimilar at about 15th digit"]
[null,null,null,null,null,null,null,{"$f":"H26=H28","v":true},true,false,true,true,true,true,true,true,true,true,true,true,false,false,true,false,true,true,false,false,false,false,false,true,true,false,true,true,true,false,false,{"$f":"AN26=AN28","v":false},true,true,false,false,false,true,true,false,false,true,false,true,false,false,true,false,false,false,true,true,true,true,false,false,false]
["Therefore:",null,null,null,null,null,"check",{"$f":"($B$31^H29*EXP(1)^-$B$31)/FACT(H29)","v":2.0611536224385595E-9},{"$f":"($B$31^I29*EXP(1)^-$B$31)/FACT(I29)","v":4.1223072448771192E-8},4.1223072448771189E-7,2.7482048299180789E-6,1.3741024149590398E-5,5.4964096598361591E-5,1.8321365532787196E-4,5.2346758665106281E-4,1.3086689666276569E-3,2.9081532591725707E-3,5.8163065183451414E-3,1.0575102760627529E-2,1.7625171267712549E-2,2.7115648104173155E-2,3.8736640148818793E-2,5.1648853531758389E-2,6.4561066914697984E-2,7.5954196370232929E-2,8.4393551522481028E-2,8.8835317392085278E-2,8.8835317392085292E-2,8.460506418293838E-2,7.6913694711762154E-2,6.6881473662401866E-2,5.5734561385334898E-2,4.4587649108267922E-2,3.429819162174455E-2,2.5406067867958928E-2,1.814719133425638E-2,1.2515304368452674E-2,8.343536245635115E-3,5.3829266100871706E-3,3.3643291313044821E-3,2.0389873523057461E-3,1.1994043248857336E-3,6.8537389993470485E-4,3.8076327774150254E-4,2.0581798796837981E-4,1.0832525682546308E-4,5.5551413756647715E-5,2.7775706878323854E-5,1.354912530649945E-5,6.4519644316664011E-6,3.0009136891471634E-6,1.3640516768850743E-6,6.0624518972669967E-7,2.635848650985651E-7,1.1216377238236811E-7,4.6734905159320076E-8,1.9075471493600014E-8,7.6301885974400101E-9,2.992230822525495E-9,1.1508580086636512E-9,4.3428604100515167E-10,1.608466818537599E-10,5.8489702492276346E-11,2.0889179461527261E-11,7.3295366531674551E-12]
[]
["If we know Poisson like:",null,null,null,null,null,"f(x)",{"$f":"_xlfn.POISSON.DIST(H29,$B$31,0)","v":2.0611536224385579E-9},{"$f":"_xlfn.POISSON.DIST(I29,$B$31,0)","v":4.1223072448771152E-8},{"$f":"_xlfn.POISSON.DIST(J29,$B$31,0)","v":4.1223072448771121E-7},2.7482048299180789E-6,1.3741024149590403E-5,5.4964096598361591E-5,1.8321365532787196E-4,5.2346758665106302E-4,1.3086689666276553E-3,2.9081532591725681E-3,5.8163065183451353E-3,1.0575102760627515E-2,1.7625171267712545E-2,2.7115648104173135E-2,3.8736640148818745E-2,5.1648853531758354E-2,6.4561066914697929E-2,7.595419637023286E-2,8.4393551522480972E-2,8.8835317392085208E-2,8.8835317392085222E-2,8.4605064182938283E-2,7.6913694711762098E-2,6.6881473662401839E-2,5.5734561385334863E-2,4.4587649108267881E-2,3.4298191621744509E-2,2.5406067867958917E-2,1.8147191334256366E-2,1.2515304368452655E-2,8.3435362456351133E-3,5.3829266100871558E-3,3.3643291313044709E-3,2.0389873523057505E-3,1.199404324885734E-3,6.8537389993470344E-4,3.8076327774150232E-4,2.0581798796837891E-4,1.0832525682546335E-4,5.5551413756647715E-5,2.7775706878323834E-5,1.3549125306499445E-5,6.4519644316664028E-6,3.0009136891471711E-6,1.3640516768850688E-6,6.0624518972670115E-7,2.6358486509856742E-7,1.1216377238236792E-7,4.6734905159320215E-8,1.9075471493599922E-8,7.6301885974399753E-9,2.9922308225254937E-9,1.1508580086636487E-9,4.3428604100515208E-10,1.6084668185375959E-10,5.8489702492276397E-11,2.0889179461527371E-11,7.3295366531674163E-12]
[null,null,null,null,null,null,"x",0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57]
["f(x) = (μxe-μ)/x!","Height & Probability",null,null,null,null,{"$f":"A36&\" = \"&ROUND(B36,4)","v":"P(x<=25) = 0"},{"$f":"IF(H29<=$B$35,H28,\"\")","v":2.0611536224385579E-9},{"$f":"IF(I29<=$B$35,I28,\"\")","v":4.1223072448771152E-8},{"$f":"IF(J29<=$B$35,J28,\"\")","v":4.1223072448771121E-7},{"$f":"IF(K29<=$B$35,K28,\"\")","v":2.7482048299180789E-6},{"$f":"IF(L29<=$B$35,L28,\"\")","v":1.3741024149590403E-5},{"$f":"IF(M29<=$B$35,M28,\"\")","v":5.4964096598361591E-5},{"$f":"IF(N29<=$B$35,N28,\"\")","v":1.8321365532787196E-4},{"$f":"IF(O29<=$B$35,O28,\"\")","v":5.2346758665106302E-4},{"$f":"IF(P29<=$B$35,P28,\"\")","v":1.3086689666276553E-3},{"$f":"IF(Q29<=$B$35,Q28,\"\")","v":2.9081532591725681E-3},{"$f":"IF(R29<=$B$35,R28,\"\")","v":5.8163065183451353E-3},{"$f":"IF(S29<=$B$35,S28,\"\")","v":1.0575102760627515E-2},{"$f":"IF(T29<=$B$35,T28,\"\")","v":1.7625171267712545E-2},{"$f":"IF(U29<=$B$35,U28,\"\")","v":2.7115648104173135E-2},{"$f":"IF(V29<=$B$35,V28,\"\")","v":3.8736640148818745E-2},{"$f":"IF(W29<=$B$35,W28,\"\")","v":5.1648853531758354E-2},{"$f":"IF(X29<=$B$35,X28,\"\")","v":6.4561066914697929E-2},{"$f":"IF(Y29<=$B$35,Y28,\"\")","v":7.595419637023286E-2},{"$f":"IF(Z29<=$B$35,Z28,\"\")","v":8.4393551522480972E-2},{"$f":"IF(AA29<=$B$35,AA28,\"\")","v":8.8835317392085208E-2},{"$f":"IF(AB29<=$B$35,AB28,\"\")","v":8.8835317392085222E-2},{"$f":"IF(AC29<=$B$35,AC28,\"\")","v":8.4605064182938283E-2},{"$f":"IF(AD29<=$B$35,AD28,\"\")","v":7.6913694711762098E-2},{"$f":"IF(AE29<=$B$35,AE28,\"\")","v":6.6881473662401839E-2},{"$f":"IF(AF29<=$B$35,AF28,\"\")","v":5.5734561385334863E-2},{"$f":"IF(AG29<=$B$35,AG28,\"\")","v":4.4587649108267881E-2},{"$f":"IF(AH29<=$B$35,AH28,\"\")","v":""},{"$f":"IF(AI29<=$B$35,AI28,\"\")","v":""},{"$f":"IF(AJ29<=$B$35,AJ28,\"\")","v":""},{"$f":"IF(AK29<=$B$35,AK28,\"\")","v":""},{"$f":"IF(AL29<=$B$35,AL28,\"\")","v":""},{"$f":"IF(AM29<=$B$35,AM28,\"\")","v":""},{"$f":"IF(AN29<=$B$35,AN28,\"\")","v":""},{"$f":"IF(AO29<=$B$35,AO28,\"\")","v":""},{"$f":"IF(AP29<=$B$35,AP28,\"\")","v":""},{"$f":"IF(AQ29<=$B$35,AQ28,\"\")","v":""},{"$f":"IF(AR29<=$B$35,AR28,\"\")","v":""},{"$f":"IF(AS29<=$B$35,AS28,\"\")","v":""},{"$f":"IF(AT29<=$B$35,AT28,\"\")","v":""},{"$f":"IF(AU29<=$B$35,AU28,\"\")","v":""},{"$f":"IF(AV29<=$B$35,AV28,\"\")","v":""},{"$f":"IF(AW29<=$B$35,AW28,\"\")","v":""},{"$f":"IF(AX29<=$B$35,AX28,\"\")","v":""},{"$f":"IF(AY29<=$B$35,AY28,\"\")","v":""},{"$f":"IF(AZ29<=$B$35,AZ28,\"\")","v":""},{"$f":"IF(BA29<=$B$35,BA28,\"\")","v":""},{"$f":"IF(BB29<=$B$35,BB28,\"\")","v":""},{"$f":"IF(BC29<=$B$35,BC28,\"\")","v":""},{"$f":"IF(BD29<=$B$35,BD28,\"\")","v":""},{"$f":"IF(BE29<=$B$35,BE28,\"\")","v":""},{"$f":"IF(BF29<=$B$35,BF28,\"\")","v":""},{"$f":"IF(BG29<=$B$35,BG28,\"\")","v":""},{"$f":"IF(BH29<=$B$35,BH28,\"\")","v":""},{"$f":"IF(BI29<=$B$35,BI28,\"\")","v":""},{"$f":"IF(BJ29<=$B$35,BJ28,\"\")","v":""},{"$f":"IF(BK29<=$B$35,BK28,\"\")","v":""},{"$f":"IF(BL29<=$B$35,BL28,\"\")","v":""},{"$f":"IF(BM29<=$B$35,BM28,\"\")","v":""}]
["μ = Expected Value = mean ",20,"visitors",{"$f":"\"per \"&B32&\" \"&C32","v":"per 1 hour"},"# occurrences in interval"]
["Time interval",1,"hour"]
[{"$f":"\"x = # \"&C31&\" \"&D31&\" to web site\"","v":"x = # visitors per 1 hour to web site"}]
[{"$f":"\"f(x) = (\"&B31&\"^x * \"&ROUND(EXP(1),4)&\"^-\"&B31&\") / X!\"","v":"f(x) = (20^x * 2.7183^-20) / X!"}]
["x",25,null,"Check"]
[{"$f":"\"P(x<=\"&B35&\")\"","v":"P(x<=25)"},null,null,{"$f":"SUMIF($H$29:$BM$29,\"<=\"&B35,$H$28:$BM$28)","v":0.88781502728203021},{"$f":"D36=B36","v":false}]
[]
["Then we can calculate mew for Exponetial:"]
["μ = Expected Value = average time between arrivals"]
["μ = Expected Value = mean =",null,"hours","Time between arrivals"]
[null,null,"minutes"]
["x = time between arrivals at store"]
[]
["And then Exponential Function:"]
[null,null,null,null,null,null,null,{"$f":"H46=H49","v":true},{"$f":"I46=I49","v":true},{"$f":"J46=J49","v":true},true,true,true,true,true,true,true,true,true,true,true,true,true,true,true,true,true,true,true,true,true,true,false,true,true,true,true,true,true,true,true,true,true,true,true,true,true,false,true,true,false,true,true,true,true,true,true,false,true,true,false,true,true,true,true,false,true,true]
["f(x) = 1/μ*e-x/μ        For x >=0","Density Function to determine Height of curve, not probability",null,null,null,null,"check",{"$f":"1/$H$48*EXP(1)^-(H50/$H$48)","v":0.33333333333333331},{"$f":"1/$H$48*EXP(1)^-(I50/$H$48)","v":0.28216057496353802},{"$f":"1/$H$48*EXP(1)^-(J50/$H$48)","v":0.23884377019126307},{"$f":"1/$H$48*EXP(1)^-(K50/$H$48)","v":0.20217688657087779},{"$f":"1/$H$48*EXP(1)^-(L50/$H$48)","v":0.17113903967753066},{"$f":"1/$H$48*EXP(1)^-(M50/$H$48)","v":0.14486606950235939},{"$f":"1/$H$48*EXP(1)^-(N50/$H$48)","v":0.12262648039048077},{"$f":"1/$H$48*EXP(1)^-(O50/$H$48)","v":0.10380107463819921},{"$f":"1/$H$48*EXP(1)^-(P50/$H$48)","v":8.7865712705242252E-2},{"$f":"1/$H$48*EXP(1)^-(Q50/$H$48)","v":7.4376720049476611E-2},{"$f":"1/$H$48*EXP(1)^-(R50/$H$48)","v":6.2958534279187267E-2},{"$f":"1/$H$48*EXP(1)^-(S50/$H$48)","v":5.32932486932313E-2},{"$f":"1/$H$48*EXP(1)^-(T50/$H$48)","v":4.5111761078870896E-2},{"$f":"1/$H$48*EXP(1)^-(U50/$H$48)","v":3.818628133089591E-2},{"$f":"1/$H$48*EXP(1)^-(V50/$H$48)","v":3.2323989288135013E-2},{"$f":"1/$H$48*EXP(1)^-(W50/$H$48)","v":2.7361666207966266E-2},{"$f":"1/$H$48*EXP(1)^-(X50/$H$48)","v":2.3161150407600514E-2},{"$f":"1/$H$48*EXP(1)^-(Y50/$H$48)","v":1.9605490547476623E-2},{"$f":"1/$H$48*EXP(1)^-(Z50/$H$48)","v":1.6595689455954649E-2},{"$f":"1/$H$48*EXP(1)^-(AA50/$H$48)","v":1.4047947836425469E-2},{"$f":"1/$H$48*EXP(1)^-(AB50/$H$48)","v":1.1891331115750796E-2},{"$f":"1/$H$48*EXP(1)^-(AC50/$H$48)","v":1.0065794474106167E-2},{"$f":"1/$H$48*EXP(1)^-(AD50/$H$48)","v":8.5205110688357996E-3},{"$f":"1/$H$48*EXP(1)^-(AE50/$H$48)","v":7.2124569064976963E-3},{"$f":"1/$H$48*EXP(1)^-(AF50/$H$48)","v":6.1052129629113935E-3},{"$f":"1/$H$48*EXP(1)^-(AG50/$H$48)","v":5.1679511996697717E-3},{"$f":"1/$H$48*EXP(1)^-(AH50/$H$48)","v":4.3745762456469887E-3},{"$f":"1/$H$48*EXP(1)^-(AI50/$H$48)","v":3.7029988460807687E-3},{"$f":"1/$H$48*EXP(1)^-(AJ50/$H$48)","v":3.1345208504984018E-3},{"$f":"1/$H$48*EXP(1)^-(AK50/$H$48)","v":2.6533146162354836E-3},{"$f":"1/$H$48*EXP(1)^-(AL50/$H$48)","v":2.2459823330284894E-3},{"$f":"1/$H$48*EXP(1)^-(AM50/$H$48)","v":1.9011829993358003E-3},{"$f":"1/$H$48*EXP(1)^-(AN50/$H$48)","v":1.6093166646104803E-3},{"$f":"1/$H$48*EXP(1)^-(AO50/$H$48)","v":1.362257146154689E-3},{"$f":"1/$H$48*EXP(1)^-(AP50/$H$48)","v":1.1531257788215861E-3},{"$f":"1/$H$48*EXP(1)^-(AQ50/$H$48)","v":9.7609989827272955E-4},{"$f":"1/$H$48*EXP(1)^-(AR50/$H$48)","v":8.2625072555545312E-4},{"$f":"1/$H$48*EXP(1)^-(AS50/$H$48)","v":6.9940613936030082E-4},{"$f":"1/$H$48*EXP(1)^-(AT50/$H$48)","v":5.9203451524479297E-4},{"$f":"1/$H$48*EXP(1)^-(AU50/$H$48)","v":5.0114639765919079E-4},{"$f":"1/$H$48*EXP(1)^-(AV50/$H$48)","v":4.242112671132693E-4},{"$f":"1/$H$48*EXP(1)^-(AW50/$H$48)","v":3.5908708510407343E-4},{"$f":"1/$H$48*EXP(1)^-(AX50/$H$48)","v":3.0396065518483882E-4},{"$f":"1/$H$48*EXP(1)^-(AY50/$H$48)","v":2.5729713969974339E-4},{"$f":"1/$H$48*EXP(1)^-(AZ50/$H$48)","v":2.1779732662246019E-4},{"$f":"1/$H$48*EXP(1)^-(BA50/$H$48)","v":1.8436145671594454E-4},{"$f":"1/$H$48*EXP(1)^-(BB50/$H$48)","v":1.5605860388425894E-4},{"$f":"1/$H$48*EXP(1)^-(BC50/$H$48)","v":1.3210075619996868E-4},{"$f":"1/$H$48*EXP(1)^-(BD50/$H$48)","v":1.1182087596750399E-4},{"$f":"1/$H$48*EXP(1)^-(BE50/$H$48)","v":9.4654327967752205E-5},{"$f":"1/$H$48*EXP(1)^-(BF50/$H$48)","v":8.0123158806504681E-5},{"$f":"1/$H$48*EXP(1)^-(BG50/$H$48)","v":6.7822789670214718E-5},{"$f":"1/$H$48*EXP(1)^-(BH50/$H$48)","v":5.741075198693671E-5},{"$f":"1/$H$48*EXP(1)^-(BI50/$H$48)","v":4.8597152369169374E-5},{"$f":"1/$H$48*EXP(1)^-(BJ50/$H$48)","v":4.1136601362226529E-5},{"$f":"1/$H$48*EXP(1)^-(BK50/$H$48)","v":3.482138127723511E-5},{"$f":"1/$H$48*EXP(1)^-(BL50/$H$48)","v":2.9475662886627671E-5},{"$f":"1/$H$48*EXP(1)^-(BM50/$H$48)","v":2.4950609962566862E-5},{"$f":"1/$H$48*EXP(1)^-(BN50/$H$48)","v":2.1120235358186554E-5},{"$f":"1/$H$48*EXP(1)^-(BO50/$H$48)","v":1.7877893256093464E-5},{"$f":"1/$H$48*EXP(1)^-(BP50/$H$48)","v":1.5133309920828292E-5}]
["P(x<=x0) = 1- e-x0/μ","Used to calculate cumulative",null,null,null,null,"mean",{"$f":"B32/B31","v":0.05},"hours"]
[{"$f":"\"f(x) = 1/\"&H47&\" * \"&ROUND(EXP(1),4)&\"^-(x / \"&H47&\") = \"","v":"f(x) = 1/0.05 * 2.7183^-(x / 0.05) = "},null,null,null,null,null,"mean",{"$f":"B32/B31*60","v":3},"minutes"]
[{"$f":"\" = \"&1/H47&\" *\"&ROUND(EXP(1),4)&\"^-\"&1/H47&\"x\"","v":" = 20 *2.7183^-20x"},null,null,null,null,null,"f(x)",{"$f":"_xlfn.EXPON.DIST(H50,1/$H$48,0)","v":0.33333333333333331},{"$f":"_xlfn.EXPON.DIST(I50,1/$H$48,0)","v":0.28216057496353802},{"$f":"_xlfn.EXPON.DIST(J50,1/$H$48,0)","v":0.23884377019126307},{"$f":"_xlfn.EXPON.DIST(K50,1/$H$48,0)","v":0.20217688657087779},{"$f":"_xlfn.EXPON.DIST(L50,1/$H$48,0)","v":0.17113903967753066},{"$f":"_xlfn.EXPON.DIST(M50,1/$H$48,0)","v":0.14486606950235942},{"$f":"_xlfn.EXPON.DIST(N50,1/$H$48,0)","v":0.12262648039048077},{"$f":"_xlfn.EXPON.DIST(O50,1/$H$48,0)","v":0.10380107463819924},{"$f":"_xlfn.EXPON.DIST(P50,1/$H$48,0)","v":8.7865712705242252E-2},{"$f":"_xlfn.EXPON.DIST(Q50,1/$H$48,0)","v":7.4376720049476597E-2},{"$f":"_xlfn.EXPON.DIST(R50,1/$H$48,0)","v":6.2958534279187281E-2},{"$f":"_xlfn.EXPON.DIST(S50,1/$H$48,0)","v":5.32932486932313E-2},{"$f":"_xlfn.EXPON.DIST(T50,1/$H$48,0)","v":4.5111761078870896E-2},{"$f":"_xlfn.EXPON.DIST(U50,1/$H$48,0)","v":3.818628133089591E-2},{"$f":"_xlfn.EXPON.DIST(V50,1/$H$48,0)","v":3.2323989288135027E-2},{"$f":"_xlfn.EXPON.DIST(W50,1/$H$48,0)","v":2.7361666207966266E-2},{"$f":"_xlfn.EXPON.DIST(X50,1/$H$48,0)","v":2.3161150407600514E-2},{"$f":"_xlfn.EXPON.DIST(Y50,1/$H$48,0)","v":1.9605490547476637E-2},{"$f":"_xlfn.EXPON.DIST(Z50,1/$H$48,0)","v":1.6595689455954646E-2},{"$f":"_xlfn.EXPON.DIST(AA50,1/$H$48,0)","v":1.4047947836425469E-2},{"$f":"_xlfn.EXPON.DIST(AB50,1/$H$48,0)","v":1.1891331115750803E-2},{"$f":"_xlfn.EXPON.DIST(AC50,1/$H$48,0)","v":1.0065794474106167E-2},{"$f":"_xlfn.EXPON.DIST(AD50,1/$H$48,0)","v":8.5205110688357996E-3},{"$f":"_xlfn.EXPON.DIST(AE50,1/$H$48,0)","v":7.2124569064976997E-3},{"$f":"_xlfn.EXPON.DIST(AF50,1/$H$48,0)","v":6.1052129629113926E-3},{"$f":"_xlfn.EXPON.DIST(AG50,1/$H$48,0)","v":5.167951199669776E-3},{"$f":"_xlfn.EXPON.DIST(AH50,1/$H$48,0)","v":4.3745762456469887E-3},{"$f":"_xlfn.EXPON.DIST(AI50,1/$H$48,0)","v":3.7029988460807687E-3},{"$f":"_xlfn.EXPON.DIST(AJ50,1/$H$48,0)","v":3.1345208504984044E-3},{"$f":"_xlfn.EXPON.DIST(AK50,1/$H$48,0)","v":2.6533146162354831E-3},{"$f":"_xlfn.EXPON.DIST(AL50,1/$H$48,0)","v":2.245982333028489E-3},{"$f":"_xlfn.EXPON.DIST(AM50,1/$H$48,0)","v":1.901182999335802E-3},{"$f":"_xlfn.EXPON.DIST(AN50,1/$H$48,0)","v":1.6093166646104803E-3},{"$f":"_xlfn.EXPON.DIST(AO50,1/$H$48,0)","v":1.3622571461546888E-3},{"$f":"_xlfn.EXPON.DIST(AP50,1/$H$48,0)","v":1.1531257788215872E-3},{"$f":"_xlfn.EXPON.DIST(AQ50,1/$H$48,0)","v":9.7609989827272955E-4},{"$f":"_xlfn.EXPON.DIST(AR50,1/$H$48,0)","v":8.2625072555545279E-4},{"$f":"_xlfn.EXPON.DIST(AS50,1/$H$48,0)","v":6.9940613936030137E-4},{"$f":"_xlfn.EXPON.DIST(AT50,1/$H$48,0)","v":5.9203451524479297E-4},{"$f":"_xlfn.EXPON.DIST(AU50,1/$H$48,0)","v":5.0114639765919079E-4},{"$f":"_xlfn.EXPON.DIST(AV50,1/$H$48,0)","v":4.2421126711326962E-4},{"$f":"_xlfn.EXPON.DIST(AW50,1/$H$48,0)","v":3.5908708510407343E-4},{"$f":"_xlfn.EXPON.DIST(AX50,1/$H$48,0)","v":3.0396065518483871E-4},{"$f":"_xlfn.EXPON.DIST(AY50,1/$H$48,0)","v":2.5729713969974361E-4},{"$f":"_xlfn.EXPON.DIST(AZ50,1/$H$48,0)","v":2.1779732662246019E-4},{"$f":"_xlfn.EXPON.DIST(BA50,1/$H$48,0)","v":1.8436145671594454E-4},{"$f":"_xlfn.EXPON.DIST(BB50,1/$H$48,0)","v":1.560586038842591E-4},{"$f":"_xlfn.EXPON.DIST(BC50,1/$H$48,0)","v":1.3210075619996868E-4},{"$f":"_xlfn.EXPON.DIST(BD50,1/$H$48,0)","v":1.1182087596750395E-4},{"$f":"_xlfn.EXPON.DIST(BE50,1/$H$48,0)","v":9.4654327967752205E-5},{"$f":"_xlfn.EXPON.DIST(BF50,1/$H$48,0)","v":8.012315880650483E-5},{"$f":"_xlfn.EXPON.DIST(BG50,1/$H$48,0)","v":6.7822789670214718E-5},{"$f":"_xlfn.EXPON.DIST(BH50,1/$H$48,0)","v":5.741075198693671E-5},{"$f":"_xlfn.EXPON.DIST(BI50,1/$H$48,0)","v":4.8597152369169469E-5},{"$f":"_xlfn.EXPON.DIST(BJ50,1/$H$48,0)","v":4.1136601362226516E-5},{"$f":"_xlfn.EXPON.DIST(BK50,1/$H$48,0)","v":3.4821381277235103E-5},{"$f":"_xlfn.EXPON.DIST(BL50,1/$H$48,0)","v":2.9475662886627725E-5},{"$f":"_xlfn.EXPON.DIST(BM50,1/$H$48,0)","v":2.4950609962566865E-5},{"$f":"_xlfn.EXPON.DIST(BN50,1/$H$48,0)","v":2.1120235358186548E-5},{"$f":"_xlfn.EXPON.DIST(BO50,1/$H$48,0)","v":1.7877893256093498E-5},{"$f":"_xlfn.EXPON.DIST(BP50,1/$H$48,0)","v":1.5133309920828285E-5}]
["x",5,null,"check",null,null,"x",0,{"$f":"+H50+0.5","v":0.5},1,{"$f":"+J50+0.5","v":1.5},2,{"$f":"+L50+0.5","v":2.5},3,{"$f":"+N50+0.5","v":3.5},4,{"$f":"+P50+0.5","v":4.5},5,{"$f":"+R50+0.5","v":5.5},6,{"$f":"+T50+0.5","v":6.5},7,{"$f":"+V50+0.5","v":7.5},8,{"$f":"+X50+0.5","v":8.5},9,{"$f":"+Z50+0.5","v":9.5},10,{"$f":"+AB50+0.5","v":10.5},11,{"$f":"+AD50+0.5","v":11.5},12,{"$f":"+AF50+0.5","v":12.5},13,{"$f":"+AH50+0.5","v":13.5},14,{"$f":"+AJ50+0.5","v":14.5},15,{"$f":"+AL50+0.5","v":15.5},16,{"$f":"+AN50+0.5","v":16.5},17,{"$f":"+AP50+0.5","v":17.5},18,{"$f":"+AR50+0.5","v":18.5},19,{"$f":"+AT50+0.5","v":19.5},20,{"$f":"+AV50+0.5","v":20.5},21,{"$f":"+AX50+0.5","v":21.5},22,{"$f":"+AZ50+0.5","v":22.5},23,{"$f":"+BB50+0.5","v":23.5},24,{"$f":"+BD50+0.5","v":24.5},25,{"$f":"+BF50+0.5","v":25.5},26,{"$f":"+BH50+0.5","v":26.5},27,{"$f":"+BJ50+0.5","v":27.5},28,{"$f":"+BL50+0.5","v":28.5},29,{"$f":"+BN50+0.5","v":29.5},30]
[{"$f":"\"P(x<=\"&B50&\")\"","v":"P(x<=5)"},null,null,{"$f":"1-EXP(1)^-(B50/H48)","v":0.81112439716243823},{"$f":"D51=B51","v":false},null,{"$f":"A51&\" = \"&ROUND(B51,4)","v":"P(x<=5) = 0"},{"$f":"IF(H50<=$B$50,H49,\"\")","v":0.33333333333333331},{"$f":"IF(I50<=$B$50,I49,\"\")","v":0.28216057496353802},{"$f":"IF(J50<=$B$50,J49,\"\")","v":0.23884377019126307},{"$f":"IF(K50<=$B$50,K49,\"\")","v":0.20217688657087779},{"$f":"IF(L50<=$B$50,L49,\"\")","v":0.17113903967753066},{"$f":"IF(M50<=$B$50,M49,\"\")","v":0.14486606950235942},{"$f":"IF(N50<=$B$50,N49,\"\")","v":0.12262648039048077},{"$f":"IF(O50<=$B$50,O49,\"\")","v":0.10380107463819924},{"$f":"IF(P50<=$B$50,P49,\"\")","v":8.7865712705242252E-2},{"$f":"IF(Q50<=$B$50,Q49,\"\")","v":7.4376720049476597E-2},{"$f":"IF(R50<=$B$50,R49,\"\")","v":6.2958534279187281E-2},{"$f":"IF(S50<=$B$50,S49,\"\")","v":""},{"$f":"IF(T50<=$B$50,T49,\"\")","v":""},{"$f":"IF(U50<=$B$50,U49,\"\")","v":""},{"$f":"IF(V50<=$B$50,V49,\"\")","v":""},{"$f":"IF(W50<=$B$50,W49,\"\")","v":""},{"$f":"IF(X50<=$B$50,X49,\"\")","v":""},{"$f":"IF(Y50<=$B$50,Y49,\"\")","v":""},{"$f":"IF(Z50<=$B$50,Z49,\"\")","v":""},{"$f":"IF(AA50<=$B$50,AA49,\"\")","v":""},{"$f":"IF(AB50<=$B$50,AB49,\"\")","v":""},{"$f":"IF(AC50<=$B$50,AC49,\"\")","v":""},{"$f":"IF(AD50<=$B$50,AD49,\"\")","v":""},{"$f":"IF(AE50<=$B$50,AE49,\"\")","v":""},{"$f":"IF(AF50<=$B$50,AF49,\"\")","v":""},{"$f":"IF(AG50<=$B$50,AG49,\"\")","v":""},{"$f":"IF(AH50<=$B$50,AH49,\"\")","v":""},{"$f":"IF(AI50<=$B$50,AI49,\"\")","v":""},{"$f":"IF(AJ50<=$B$50,AJ49,\"\")","v":""},{"$f":"IF(AK50<=$B$50,AK49,\"\")","v":""},{"$f":"IF(AL50<=$B$50,AL49,\"\")","v":""},{"$f":"IF(AM50<=$B$50,AM49,\"\")","v":""},{"$f":"IF(AN50<=$B$50,AN49,\"\")","v":""},{"$f":"IF(AO50<=$B$50,AO49,\"\")","v":""},{"$f":"IF(AP50<=$B$50,AP49,\"\")","v":""},{"$f":"IF(AQ50<=$B$50,AQ49,\"\")","v":""},{"$f":"IF(AR50<=$B$50,AR49,\"\")","v":""},{"$f":"IF(AS50<=$B$50,AS49,\"\")","v":""},{"$f":"IF(AT50<=$B$50,AT49,\"\")","v":""},{"$f":"IF(AU50<=$B$50,AU49,\"\")","v":""},{"$f":"IF(AV50<=$B$50,AV49,\"\")","v":""},{"$f":"IF(AW50<=$B$50,AW49,\"\")","v":""},{"$f":"IF(AX50<=$B$50,AX49,\"\")","v":""},{"$f":"IF(AY50<=$B$50,AY49,\"\")","v":""},{"$f":"IF(AZ50<=$B$50,AZ49,\"\")","v":""},{"$f":"IF(BA50<=$B$50,BA49,\"\")","v":""},{"$f":"IF(BB50<=$B$50,BB49,\"\")","v":""},{"$f":"IF(BC50<=$B$50,BC49,\"\")","v":""},{"$f":"IF(BD50<=$B$50,BD49,\"\")","v":""},{"$f":"IF(BE50<=$B$50,BE49,\"\")","v":""},{"$f":"IF(BF50<=$B$50,BF49,\"\")","v":""},{"$f":"IF(BG50<=$B$50,BG49,\"\")","v":""},{"$f":"IF(BH50<=$B$50,BH49,\"\")","v":""},{"$f":"IF(BI50<=$B$50,BI49,\"\")","v":""},{"$f":"IF(BJ50<=$B$50,BJ49,\"\")","v":""},{"$f":"IF(BK50<=$B$50,BK49,\"\")","v":""},{"$f":"IF(BL50<=$B$50,BL49,\"\")","v":""},{"$f":"IF(BM50<=$B$50,BM49,\"\")","v":""},{"$f":"IF(BN50<=$B$50,BN49,\"\")","v":""},{"$f":"IF(BO50<=$B$50,BO49,\"\")","v":""},{"$f":"IF(BP50<=$B$50,BP49,\"\")","v":""}]

{"sheet":"P&E (an)","index":3,"n_rows":51,"n_cols":68,"rows_kept":51,"cut":false,"hidden":false,"merged":[]}
["Poisson","POISSON.DIST"]
["Discrete Random Variable"]
["# of occurrences in an interval (time or space)"]
["f(x) = (μxe-μ)/x!","Height & Probability"]
["f(x)","probability of x occurrences in an interval"]
["X = Random Discrete Variable","# of occurrences in interval"]
["μ = Expected Value = Mean =","Expected Value of Mean = # of occurrences in an interval"]
["x values = 0,1,2,3,…"]
["without upper limit (but the probability is nil in the upper numbers)"]
["Mean = Variance"]
[]
["Exponential","EXPON.DIST"]
["Continuous Random Variable"]
["Probability of length of interval (time or space) between occurrences"]
["f(x) = (1/μ)*e-x/μ        For x >=0","Density Function to determine Height of curve, not probability"]
["P(x<=x0) = 1- e-x0/μ","Used to calculate cumulative"]
["P(x)","Probability of length of interval (time or space)"]
["X = Continuous Random Variable","Length of interval between two occurrences  (time or space - minutes/hours or feet/miles)"]
["μ = Mean = Expected Value =","Expected Value of Mean = time between occurrences (1 arrival and next or beg and end)"]
["x values > = 0"]
["without upper limit (but the probability is nil in the upper numbers)"]
["Mean = Standard Deviation"]
[]
["If Poisson Distribution describes # of occurrences in an internal, then the Exponential Distribution describes length of interval (probability of)",null,null,null,null,null,null,null,null,"Falses are disimilar at about 15th digit"]
[null,null,null,null,null,null,null,{"$f":"H26=H28","v":true},true,false,true,true,true,true,true,true,true,true,true,true,false,false,true,false,true,true,false,false,false,false,false,true,true,false,true,true,true,false,false,false,true,true,false,false,false,true,true,false,false,true,false,true,false,false,true,false,false,false,true,true,true,true,false,false,false]
["Therefore:",null,null,null,null,null,"check",{"$f":"($B$31^H29*EXP(1)^-$B$31)/FACT(H29)","v":2.0611536224385595E-9},{"$f":"($B$31^I29*EXP(1)^-$B$31)/FACT(I29)","v":4.1223072448771192E-8},4.1223072448771189E-7,2.7482048299180789E-6,1.3741024149590398E-5,5.4964096598361591E-5,1.8321365532787196E-4,5.2346758665106281E-4,1.3086689666276569E-3,2.9081532591725707E-3,5.8163065183451414E-3,1.0575102760627529E-2,1.7625171267712549E-2,2.7115648104173155E-2,3.8736640148818793E-2,5.1648853531758389E-2,6.4561066914697984E-2,7.5954196370232929E-2,8.4393551522481028E-2,8.8835317392085278E-2,8.8835317392085292E-2,8.460506418293838E-2,7.6913694711762154E-2,6.6881473662401866E-2,5.5734561385334898E-2,4.4587649108267922E-2,3.429819162174455E-2,2.5406067867958928E-2,1.814719133425638E-2,1.2515304368452674E-2,8.343536245635115E-3,5.3829266100871706E-3,3.3643291313044821E-3,2.0389873523057461E-3,1.1994043248857336E-3,6.8537389993470485E-4,3.8076327774150254E-4,2.0581798796837981E-4,1.0832525682546308E-4,5.5551413756647715E-5,2.7775706878323854E-5,1.354912530649945E-5,6.4519644316664011E-6,3.0009136891471634E-6,1.3640516768850743E-6,6.0624518972669967E-7,2.635848650985651E-7,1.1216377238236811E-7,4.6734905159320076E-8,1.9075471493600014E-8,7.6301885974400101E-9,2.992230822525495E-9,1.1508580086636512E-9,4.3428604100515167E-10,1.608466818537599E-10,5.8489702492276346E-11,2.0889179461527261E-11,7.3295366531674551E-12]
[]
["If we know Poisson like:",null,null,null,null,null,"f(x)",{"$f":"_xlfn.POISSON.DIST(H29,$B$31,0)","v":2.0611536224385579E-9},{"$f":"_xlfn.POISSON.DIST(I29,$B$31,0)","v":4.1223072448771152E-8},{"$f":"_xlfn.POISSON.DIST(J29,$B$31,0)","v":4.1223072448771121E-7},2.7482048299180789E-6,1.3741024149590403E-5,5.4964096598361591E-5,1.8321365532787196E-4,5.2346758665106302E-4,1.3086689666276553E-3,2.9081532591725681E-3,5.8163065183451353E-3,1.0575102760627515E-2,1.7625171267712545E-2,2.7115648104173135E-2,3.8736640148818745E-2,5.1648853531758354E-2,6.4561066914697929E-2,7.595419637023286E-2,8.4393551522480972E-2,8.8835317392085208E-2,8.8835317392085222E-2,8.4605064182938283E-2,7.6913694711762098E-2,6.6881473662401839E-2,5.5734561385334863E-2,4.4587649108267881E-2,3.4298191621744509E-2,2.5406067867958917E-2,1.8147191334256366E-2,1.2515304368452655E-2,8.3435362456351133E-3,5.3829266100871558E-3,3.3643291313044709E-3,2.0389873523057505E-3,1.199404324885734E-3,6.8537389993470344E-4,3.8076327774150232E-4,2.0581798796837891E-4,1.0832525682546335E-4,5.5551413756647715E-5,2.7775706878323834E-5,1.3549125306499445E-5,6.4519644316664028E-6,3.0009136891471711E-6,1.3640516768850688E-6,6.0624518972670115E-7,2.6358486509856742E-7,1.1216377238236792E-7,4.6734905159320215E-8,1.9075471493599922E-8,7.6301885974399753E-9,2.9922308225254937E-9,1.1508580086636487E-9,4.3428604100515208E-10,1.6084668185375959E-10,5.8489702492276397E-11,2.0889179461527371E-11,7.3295366531674163E-12]
[null,null,null,null,null,null,"x",0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57]
["f(x) = (μxe-μ)/x!","Height & Probability",null,null,null,null,{"$f":"A36&\" = \"&ROUND(B36,4)","v":"P(x<=25) = 0.8878"},{"$f":"IF(H29<=$B$35,H28,\"\")","v":2.0611536224385579E-9},{"$f":"IF(I29<=$B$35,I28,\"\")","v":4.1223072448771152E-8},{"$f":"IF(J29<=$B$35,J28,\"\")","v":4.1223072448771121E-7},{"$f":"IF(K29<=$B$35,K28,\"\")","v":2.7482048299180789E-6},{"$f":"IF(L29<=$B$35,L28,\"\")","v":1.3741024149590403E-5},{"$f":"IF(M29<=$B$35,M28,\"\")","v":5.4964096598361591E-5},{"$f":"IF(N29<=$B$35,N28,\"\")","v":1.8321365532787196E-4},{"$f":"IF(O29<=$B$35,O28,\"\")","v":5.2346758665106302E-4},{"$f":"IF(P29<=$B$35,P28,\"\")","v":1.3086689666276553E-3},{"$f":"IF(Q29<=$B$35,Q28,\"\")","v":2.9081532591725681E-3},{"$f":"IF(R29<=$B$35,R28,\"\")","v":5.8163065183451353E-3},{"$f":"IF(S29<=$B$35,S28,\"\")","v":1.0575102760627515E-2},{"$f":"IF(T29<=$B$35,T28,\"\")","v":1.7625171267712545E-2},{"$f":"IF(U29<=$B$35,U28,\"\")","v":2.7115648104173135E-2},{"$f":"IF(V29<=$B$35,V28,\"\")","v":3.8736640148818745E-2},{"$f":"IF(W29<=$B$35,W28,\"\")","v":5.1648853531758354E-2},{"$f":"IF(X29<=$B$35,X28,\"\")","v":6.4561066914697929E-2},{"$f":"IF(Y29<=$B$35,Y28,\"\")","v":7.595419637023286E-2},{"$f":"IF(Z29<=$B$35,Z28,\"\")","v":8.4393551522480972E-2},{"$f":"IF(AA29<=$B$35,AA28,\"\")","v":8.8835317392085208E-2},{"$f":"IF(AB29<=$B$35,AB28,\"\")","v":8.8835317392085222E-2},{"$f":"IF(AC29<=$B$35,AC28,\"\")","v":8.4605064182938283E-2},{"$f":"IF(AD29<=$B$35,AD28,\"\")","v":7.6913694711762098E-2},{"$f":"IF(AE29<=$B$35,AE28,\"\")","v":6.6881473662401839E-2},{"$f":"IF(AF29<=$B$35,AF28,\"\")","v":5.5734561385334863E-2},{"$f":"IF(AG29<=$B$35,AG28,\"\")","v":4.4587649108267881E-2},{"$f":"IF(AH29<=$B$35,AH28,\"\")","v":""},{"$f":"IF(AI29<=$B$35,AI28,\"\")","v":""},{"$f":"IF(AJ29<=$B$35,AJ28,\"\")","v":""},{"$f":"IF(AK29<=$B$35,AK28,\"\")","v":""},{"$f":"IF(AL29<=$B$35,AL28,\"\")","v":""},{"$f":"IF(AM29<=$B$35,AM28,\"\")","v":""},{"$f":"IF(AN29<=$B$35,AN28,\"\")","v":""},{"$f":"IF(AO29<=$B$35,AO28,\"\")","v":""},{"$f":"IF(AP29<=$B$35,AP28,\"\")","v":""},{"$f":"IF(AQ29<=$B$35,AQ28,\"\")","v":""},{"$f":"IF(AR29<=$B$35,AR28,\"\")","v":""},{"$f":"IF(AS29<=$B$35,AS28,\"\")","v":""},{"$f":"IF(AT29<=$B$35,AT28,\"\")","v":""},{"$f":"IF(AU29<=$B$35,AU28,\"\")","v":""},{"$f":"IF(AV29<=$B$35,AV28,\"\")","v":""},{"$f":"IF(AW29<=$B$35,AW28,\"\")","v":""},{"$f":"IF(AX29<=$B$35,AX28,\"\")","v":""},{"$f":"IF(AY29<=$B$35,AY28,\"\")","v":""},{"$f":"IF(AZ29<=$B$35,AZ28,\"\")","v":""},{"$f":"IF(BA29<=$B$35,BA28,\"\")","v":""},{"$f":"IF(BB29<=$B$35,BB28,\"\")","v":""},{"$f":"IF(BC29<=$B$35,BC28,\"\")","v":""},{"$f":"IF(BD29<=$B$35,BD28,\"\")","v":""},{"$f":"IF(BE29<=$B$35,BE28,\"\")","v":""},{"$f":"IF(BF29<=$B$35,BF28,\"\")","v":""},{"$f":"IF(BG29<=$B$35,BG28,\"\")","v":""},{"$f":"IF(BH29<=$B$35,BH28,\"\")","v":""},{"$f":"IF(BI29<=$B$35,BI28,\"\")","v":""},{"$f":"IF(BJ29<=$B$35,BJ28,\"\")","v":""},{"$f":"IF(BK29<=$B$35,BK28,\"\")","v":""},{"$f":"IF(BL29<=$B$35,BL28,\"\")","v":""},{"$f":"IF(BM29<=$B$35,BM28,\"\")","v":""}]
["μ = Expected Value = mean ",20,"visitors",{"$f":"\"per \"&B32&\" \"&C32","v":"per 1 hour"},"# occurrences in interval"]
["Time interval",1,"hour"]
[{"$f":"\"x = # \"&C31&\" \"&D31&\" to web site\"","v":"x = # visitors per 1 hour to web site"}]
[{"$f":"\"f(x) = (\"&B31&\"^x * \"&ROUND(EXP(1),4)&\"^-\"&B31&\") / X!\"","v":"f(x) = (20^x * 2.7183^-20) / X!"}]
["x",25,null,"Check"]
[{"$f":"\"P(x<=\"&B35&\")\"","v":"P(x<=25)"},{"$f":"_xlfn.POISSON.DIST(B35,B31,1)","v":0.88781502728203021},null,{"$f":"SUMIF($H$29:$BM$29,\"<=\"&B35,$H$28:$BM$28)","v":0.88781502728203021},{"$f":"D36=B36","v":true}]
[]
["Then we can calculate mew for Exponetial:"]
["μ = Expected Value = average time between arrivals"]
["μ = Expected Value = mean =",{"$f":"B32/B31","v":0.05},"hours","Time between arrivals"]
[null,{"$f":"B40*60","v":3},"minutes"]
["x = time between arrivals at store"]
[]
["And then Exponential Function:"]
[null,null,null,null,null,null,null,{"$f":"H46=H49","v":true},{"$f":"I46=I49","v":true},{"$f":"J46=J49","v":true},true,true,true,true,true,true,true,true,true,true,true,true,true,true,true,true,true,true,true,true,true,true,false,true,true,true,true,true,true,true,true,true,true,true,true,true,true,false,true,true,false,true,true,true,true,true,true,false,true,true,false,true,true,true,true,false,true,true]
["f(x) = 1/μ*e-x/μ        For x >=0","Density Function to determine Height of curve, not probability",null,null,null,null,"check",{"$f":"1/$H$48*EXP(1)^-(H50/$H$48)","v":0.33333333333333331},{"$f":"1/$H$48*EXP(1)^-(I50/$H$48)","v":0.28216057496353802},{"$f":"1/$H$48*EXP(1)^-(J50/$H$48)","v":0.23884377019126307},{"$f":"1/$H$48*EXP(1)^-(K50/$H$48)","v":0.20217688657087779},{"$f":"1/$H$48*EXP(1)^-(L50/$H$48)","v":0.17113903967753066},{"$f":"1/$H$48*EXP(1)^-(M50/$H$48)","v":0.14486606950235939},{"$f":"1/$H$48*EXP(1)^-(N50/$H$48)","v":0.12262648039048077},{"$f":"1/$H$48*EXP(1)^-(O50/$H$48)","v":0.10380107463819921},{"$f":"1/$H$48*EXP(1)^-(P50/$H$48)","v":8.7865712705242252E-2},{"$f":"1/$H$48*EXP(1)^-(Q50/$H$48)","v":7.4376720049476611E-2},{"$f":"1/$H$48*EXP(1)^-(R50/$H$48)","v":6.2958534279187267E-2},{"$f":"1/$H$48*EXP(1)^-(S50/$H$48)","v":5.32932486932313E-2},{"$f":"1/$H$48*EXP(1)^-(T50/$H$48)","v":4.5111761078870896E-2},{"$f":"1/$H$48*EXP(1)^-(U50/$H$48)","v":3.818628133089591E-2},{"$f":"1/$H$48*EXP(1)^-(V50/$H$48)","v":3.2323989288135013E-2},{"$f":"1/$H$48*EXP(1)^-(W50/$H$48)","v":2.7361666207966266E-2},{"$f":"1/$H$48*EXP(1)^-(X50/$H$48)","v":2.3161150407600514E-2},{"$f":"1/$H$48*EXP(1)^-(Y50/$H$48)","v":1.9605490547476623E-2},{"$f":"1/$H$48*EXP(1)^-(Z50/$H$48)","v":1.6595689455954649E-2},{"$f":"1/$H$48*EXP(1)^-(AA50/$H$48)","v":1.4047947836425469E-2},{"$f":"1/$H$48*EXP(1)^-(AB50/$H$48)","v":1.1891331115750796E-2},{"$f":"1/$H$48*EXP(1)^-(AC50/$H$48)","v":1.0065794474106167E-2},{"$f":"1/$H$48*EXP(1)^-(AD50/$H$48)","v":8.5205110688357996E-3},{"$f":"1/$H$48*EXP(1)^-(AE50/$H$48)","v":7.2124569064976963E-3},{"$f":"1/$H$48*EXP(1)^-(AF50/$H$48)","v":6.1052129629113935E-3},{"$f":"1/$H$48*EXP(1)^-(AG50/$H$48)","v":5.1679511996697717E-3},{"$f":"1/$H$48*EXP(1)^-(AH50/$H$48)","v":4.3745762456469887E-3},{"$f":"1/$H$48*EXP(1)^-(AI50/$H$48)","v":3.7029988460807687E-3},{"$f":"1/$H$48*EXP(1)^-(AJ50/$H$48)","v":3.1345208504984018E-3},{"$f":"1/$H$48*EXP(1)^-(AK50/$H$48)","v":2.6533146162354836E-3},{"$f":"1/$H$48*EXP(1)^-(AL50/$H$48)","v":2.2459823330284894E-3},{"$f":"1/$H$48*EXP(1)^-(AM50/$H$48)","v":1.9011829993358003E-3},{"$f":"1/$H$48*EXP(1)^-(AN50/$H$48)","v":1.6093166646104803E-3},{"$f":"1/$H$48*EXP(1)^-(AO50/$H$48)","v":1.362257146154689E-3},{"$f":"1/$H$48*EXP(1)^-(AP50/$H$48)","v":1.1531257788215861E-3},{"$f":"1/$H$48*EXP(1)^-(AQ50/$H$48)","v":9.7609989827272955E-4},{"$f":"1/$H$48*EXP(1)^-(AR50/$H$48)","v":8.2625072555545312E-4},{"$f":"1/$H$48*EXP(1)^-(AS50/$H$48)","v":6.9940613936030082E-4},{"$f":"1/$H$48*EXP(1)^-(AT50/$H$48)","v":5.9203451524479297E-4},{"$f":"1/$H$48*EXP(1)^-(AU50/$H$48)","v":5.0114639765919079E-4},{"$f":"1/$H$48*EXP(1)^-(AV50/$H$48)","v":4.242112671132693E-4},{"$f":"1/$H$48*EXP(1)^-(AW50/$H$48)","v":3.5908708510407343E-4},{"$f":"1/$H$48*EXP(1)^-(AX50/$H$48)","v":3.0396065518483882E-4},{"$f":"1/$H$48*EXP(1)^-(AY50/$H$48)","v":2.5729713969974339E-4},{"$f":"1/$H$48*EXP(1)^-(AZ50/$H$48)","v":2.1779732662246019E-4},{"$f":"1/$H$48*EXP(1)^-(BA50/$H$48)","v":1.8436145671594454E-4},{"$f":"1/$H$48*EXP(1)^-(BB50/$H$48)","v":1.5605860388425894E-4},{"$f":"1/$H$48*EXP(1)^-(BC50/$H$48)","v":1.3210075619996868E-4},{"$f":"1/$H$48*EXP(1)^-(BD50/$H$48)","v":1.1182087596750399E-4},{"$f":"1/$H$48*EXP(1)^-(BE50/$H$48)","v":9.4654327967752205E-5},{"$f":"1/$H$48*EXP(1)^-(BF50/$H$48)","v":8.0123158806504681E-5},{"$f":"1/$H$48*EXP(1)^-(BG50/$H$48)","v":6.7822789670214718E-5},{"$f":"1/$H$48*EXP(1)^-(BH50/$H$48)","v":5.741075198693671E-5},{"$f":"1/$H$48*EXP(1)^-(BI50/$H$48)","v":4.8597152369169374E-5},{"$f":"1/$H$48*EXP(1)^-(BJ50/$H$48)","v":4.1136601362226529E-5},{"$f":"1/$H$48*EXP(1)^-(BK50/$H$48)","v":3.482138127723511E-5},{"$f":"1/$H$48*EXP(1)^-(BL50/$H$48)","v":2.9475662886627671E-5},{"$f":"1/$H$48*EXP(1)^-(BM50/$H$48)","v":2.4950609962566862E-5},{"$f":"1/$H$48*EXP(1)^-(BN50/$H$48)","v":2.1120235358186554E-5},{"$f":"1/$H$48*EXP(1)^-(BO50/$H$48)","v":1.7877893256093464E-5},{"$f":"1/$H$48*EXP(1)^-(BP50/$H$48)","v":1.5133309920828292E-5}]
["P(x<=x0) = 1- e-x0/μ","Used to calculate cumulative",null,null,null,null,"mean",{"$f":"B32/B31","v":0.05},"hours"]
[{"$f":"\"f(x) = 1/\"&H47&\" * \"&ROUND(EXP(1),4)&\"^-(x / \"&H47&\") = \"","v":"f(x) = 1/0.05 * 2.7183^-(x / 0.05) = "},null,null,null,null,null,"mean",{"$f":"B32/B31*60","v":3},"minutes"]
[{"$f":"\" = \"&1/H47&\" *\"&ROUND(EXP(1),4)&\"^-\"&1/H47&\"x\"","v":" = 20 *2.7183^-20x"},null,null,null,null,null,"f(x)",{"$f":"_xlfn.EXPON.DIST(H50,1/$H$48,0)","v":0.33333333333333331},{"$f":"_xlfn.EXPON.DIST(I50,1/$H$48,0)","v":0.28216057496353802},{"$f":"_xlfn.EXPON.DIST(J50,1/$H$48,0)","v":0.23884377019126307},{"$f":"_xlfn.EXPON.DIST(K50,1/$H$48,0)","v":0.20217688657087779},{"$f":"_xlfn.EXPON.DIST(L50,1/$H$48,0)","v":0.17113903967753066},{"$f":"_xlfn.EXPON.DIST(M50,1/$H$48,0)","v":0.14486606950235942},{"$f":"_xlfn.EXPON.DIST(N50,1/$H$48,0)","v":0.12262648039048077},{"$f":"_xlfn.EXPON.DIST(O50,1/$H$48,0)","v":0.10380107463819924},{"$f":"_xlfn.EXPON.DIST(P50,1/$H$48,0)","v":8.7865712705242252E-2},{"$f":"_xlfn.EXPON.DIST(Q50,1/$H$48,0)","v":7.4376720049476597E-2},{"$f":"_xlfn.EXPON.DIST(R50,1/$H$48,0)","v":6.2958534279187281E-2},{"$f":"_xlfn.EXPON.DIST(S50,1/$H$48,0)","v":5.32932486932313E-2},{"$f":"_xlfn.EXPON.DIST(T50,1/$H$48,0)","v":4.5111761078870896E-2},{"$f":"_xlfn.EXPON.DIST(U50,1/$H$48,0)","v":3.818628133089591E-2},{"$f":"_xlfn.EXPON.DIST(V50,1/$H$48,0)","v":3.2323989288135027E-2},{"$f":"_xlfn.EXPON.DIST(W50,1/$H$48,0)","v":2.7361666207966266E-2},{"$f":"_xlfn.EXPON.DIST(X50,1/$H$48,0)","v":2.3161150407600514E-2},{"$f":"_xlfn.EXPON.DIST(Y50,1/$H$48,0)","v":1.9605490547476637E-2},{"$f":"_xlfn.EXPON.DIST(Z50,1/$H$48,0)","v":1.6595689455954646E-2},{"$f":"_xlfn.EXPON.DIST(AA50,1/$H$48,0)","v":1.4047947836425469E-2},{"$f":"_xlfn.EXPON.DIST(AB50,1/$H$48,0)","v":1.1891331115750803E-2},{"$f":"_xlfn.EXPON.DIST(AC50,1/$H$48,0)","v":1.0065794474106167E-2},{"$f":"_xlfn.EXPON.DIST(AD50,1/$H$48,0)","v":8.5205110688357996E-3},{"$f":"_xlfn.EXPON.DIST(AE50,1/$H$48,0)","v":7.2124569064976997E-3},{"$f":"_xlfn.EXPON.DIST(AF50,1/$H$48,0)","v":6.1052129629113926E-3},{"$f":"_xlfn.EXPON.DIST(AG50,1/$H$48,0)","v":5.167951199669776E-3},{"$f":"_xlfn.EXPON.DIST(AH50,1/$H$48,0)","v":4.3745762456469887E-3},{"$f":"_xlfn.EXPON.DIST(AI50,1/$H$48,0)","v":3.7029988460807687E-3},{"$f":"_xlfn.EXPON.DIST(AJ50,1/$H$48,0)","v":3.1345208504984044E-3},{"$f":"_xlfn.EXPON.DIST(AK50,1/$H$48,0)","v":2.6533146162354831E-3},{"$f":"_xlfn.EXPON.DIST(AL50,1/$H$48,0)","v":2.245982333028489E-3},{"$f":"_xlfn.EXPON.DIST(AM50,1/$H$48,0)","v":1.901182999335802E-3},{"$f":"_xlfn.EXPON.DIST(AN50,1/$H$48,0)","v":1.6093166646104803E-3},{"$f":"_xlfn.EXPON.DIST(AO50,1/$H$48,0)","v":1.3622571461546888E-3},{"$f":"_xlfn.EXPON.DIST(AP50,1/$H$48,0)","v":1.1531257788215872E-3},{"$f":"_xlfn.EXPON.DIST(AQ50,1/$H$48,0)","v":9.7609989827272955E-4},{"$f":"_xlfn.EXPON.DIST(AR50,1/$H$48,0)","v":8.2625072555545279E-4},{"$f":"_xlfn.EXPON.DIST(AS50,1/$H$48,0)","v":6.9940613936030137E-4},{"$f":"_xlfn.EXPON.DIST(AT50,1/$H$48,0)","v":5.9203451524479297E-4},{"$f":"_xlfn.EXPON.DIST(AU50,1/$H$48,0)","v":5.0114639765919079E-4},{"$f":"_xlfn.EXPON.DIST(AV50,1/$H$48,0)","v":4.2421126711326962E-4},{"$f":"_xlfn.EXPON.DIST(AW50,1/$H$48,0)","v":3.5908708510407343E-4},{"$f":"_xlfn.EXPON.DIST(AX50,1/$H$48,0)","v":3.0396065518483871E-4},{"$f":"_xlfn.EXPON.DIST(AY50,1/$H$48,0)","v":2.5729713969974361E-4},{"$f":"_xlfn.EXPON.DIST(AZ50,1/$H$48,0)","v":2.1779732662246019E-4},{"$f":"_xlfn.EXPON.DIST(BA50,1/$H$48,0)","v":1.8436145671594454E-4},{"$f":"_xlfn.EXPON.DIST(BB50,1/$H$48,0)","v":1.560586038842591E-4},{"$f":"_xlfn.EXPON.DIST(BC50,1/$H$48,0)","v":1.3210075619996868E-4},{"$f":"_xlfn.EXPON.DIST(BD50,1/$H$48,0)","v":1.1182087596750395E-4},{"$f":"_xlfn.EXPON.DIST(BE50,1/$H$48,0)","v":9.4654327967752205E-5},{"$f":"_xlfn.EXPON.DIST(BF50,1/$H$48,0)","v":8.012315880650483E-5},{"$f":"_xlfn.EXPON.DIST(BG50,1/$H$48,0)","v":6.7822789670214718E-5},{"$f":"_xlfn.EXPON.DIST(BH50,1/$H$48,0)","v":5.741075198693671E-5},{"$f":"_xlfn.EXPON.DIST(BI50,1/$H$48,0)","v":4.8597152369169469E-5},{"$f":"_xlfn.EXPON.DIST(BJ50,1/$H$48,0)","v":4.1136601362226516E-5},{"$f":"_xlfn.EXPON.DIST(BK50,1/$H$48,0)","v":3.4821381277235103E-5},{"$f":"_xlfn.EXPON.DIST(BL50,1/$H$48,0)","v":2.9475662886627725E-5},{"$f":"_xlfn.EXPON.DIST(BM50,1/$H$48,0)","v":2.4950609962566865E-5},{"$f":"_xlfn.EXPON.DIST(BN50,1/$H$48,0)","v":2.1120235358186548E-5},{"$f":"_xlfn.EXPON.DIST(BO50,1/$H$48,0)","v":1.7877893256093498E-5},{"$f":"_xlfn.EXPON.DIST(BP50,1/$H$48,0)","v":1.5133309920828285E-5}]
["x",5,null,"check",null,null,"x",0,{"$f":"+H50+0.5","v":0.5},1,{"$f":"+J50+0.5","v":1.5},2,{"$f":"+L50+0.5","v":2.5},3,{"$f":"+N50+0.5","v":3.5},4,{"$f":"+P50+0.5","v":4.5},5,{"$f":"+R50+0.5","v":5.5},6,{"$f":"+T50+0.5","v":6.5},7,{"$f":"+V50+0.5","v":7.5},8,{"$f":"+X50+0.5","v":8.5},9,{"$f":"+Z50+0.5","v":9.5},10,{"$f":"+AB50+0.5","v":10.5},11,{"$f":"+AD50+0.5","v":11.5},12,{"$f":"+AF50+0.5","v":12.5},13,{"$f":"+AH50+0.5","v":13.5},14,{"$f":"+AJ50+0.5","v":14.5},15,{"$f":"+AL50+0.5","v":15.5},16,{"$f":"+AN50+0.5","v":16.5},17,{"$f":"+AP50+0.5","v":17.5},18,{"$f":"+AR50+0.5","v":18.5},19,{"$f":"+AT50+0.5","v":19.5},20,{"$f":"+AV50+0.5","v":20.5},21,{"$f":"+AX50+0.5","v":21.5},22,{"$f":"+AZ50+0.5","v":22.5},23,{"$f":"+BB50+0.5","v":23.5},24,{"$f":"+BD50+0.5","v":24.5},25,{"$f":"+BF50+0.5","v":25.5},26,{"$f":"+BH50+0.5","v":26.5},27,{"$f":"+BJ50+0.5","v":27.5},28,{"$f":"+BL50+0.5","v":28.5},29,{"$f":"+BN50+0.5","v":29.5},30]
[{"$f":"\"P(x<=\"&B50&\")\"","v":"P(x<=5)"},{"$f":"_xlfn.EXPON.DIST(B50,1/B41,1)","v":0.81112439716243812},null,{"$f":"1-EXP(1)^-(B50/H48)","v":0.81112439716243823},{"$f":"D51=B51","v":true},null,{"$f":"A51&\" = \"&ROUND(B51,4)","v":"P(x<=5) = 0.8111"},{"$f":"IF(H50<=$B$50,H49,\"\")","v":0.33333333333333331},{"$f":"IF(I50<=$B$50,I49,\"\")","v":0.28216057496353802},{"$f":"IF(J50<=$B$50,J49,\"\")","v":0.23884377019126307},{"$f":"IF(K50<=$B$50,K49,\"\")","v":0.20217688657087779},{"$f":"IF(L50<=$B$50,L49,\"\")","v":0.17113903967753066},{"$f":"IF(M50<=$B$50,M49,\"\")","v":0.14486606950235942},{"$f":"IF(N50<=$B$50,N49,\"\")","v":0.12262648039048077},{"$f":"IF(O50<=$B$50,O49,\"\")","v":0.10380107463819924},{"$f":"IF(P50<=$B$50,P49,\"\")","v":8.7865712705242252E-2},{"$f":"IF(Q50<=$B$50,Q49,\"\")","v":7.4376720049476597E-2},{"$f":"IF(R50<=$B$50,R49,\"\")","v":6.2958534279187281E-2},{"$f":"IF(S50<=$B$50,S49,\"\")","v":""},{"$f":"IF(T50<=$B$50,T49,\"\")","v":""},{"$f":"IF(U50<=$B$50,U49,\"\")","v":""},{"$f":"IF(V50<=$B$50,V49,\"\")","v":""},{"$f":"IF(W50<=$B$50,W49,\"\")","v":""},{"$f":"IF(X50<=$B$50,X49,\"\")","v":""},{"$f":"IF(Y50<=$B$50,Y49,\"\")","v":""},{"$f":"IF(Z50<=$B$50,Z49,\"\")","v":""},{"$f":"IF(AA50<=$B$50,AA49,\"\")","v":""},{"$f":"IF(AB50<=$B$50,AB49,\"\")","v":""},{"$f":"IF(AC50<=$B$50,AC49,\"\")","v":""},{"$f":"IF(AD50<=$B$50,AD49,\"\")","v":""},{"$f":"IF(AE50<=$B$50,AE49,\"\")","v":""},{"$f":"IF(AF50<=$B$50,AF49,\"\")","v":""},{"$f":"IF(AG50<=$B$50,AG49,\"\")","v":""},{"$f":"IF(AH50<=$B$50,AH49,\"\")","v":""},{"$f":"IF(AI50<=$B$50,AI49,\"\")","v":""},{"$f":"IF(AJ50<=$B$50,AJ49,\"\")","v":""},{"$f":"IF(AK50<=$B$50,AK49,\"\")","v":""},{"$f":"IF(AL50<=$B$50,AL49,\"\")","v":""},{"$f":"IF(AM50<=$B$50,AM49,\"\")","v":""},{"$f":"IF(AN50<=$B$50,AN49,\"\")","v":""},{"$f":"IF(AO50<=$B$50,AO49,\"\")","v":""},{"$f":"IF(AP50<=$B$50,AP49,\"\")","v":""},{"$f":"IF(AQ50<=$B$50,AQ49,\"\")","v":""},{"$f":"IF(AR50<=$B$50,AR49,\"\")","v":""},{"$f":"IF(AS50<=$B$50,AS49,\"\")","v":""},{"$f":"IF(AT50<=$B$50,AT49,\"\")","v":""},{"$f":"IF(AU50<=$B$50,AU49,\"\")","v":""},{"$f":"IF(AV50<=$B$50,AV49,\"\")","v":""},{"$f":"IF(AW50<=$B$50,AW49,\"\")","v":""},{"$f":"IF(AX50<=$B$50,AX49,\"\")","v":""},{"$f":"IF(AY50<=$B$50,AY49,\"\")","v":""},{"$f":"IF(AZ50<=$B$50,AZ49,\"\")","v":""},{"$f":"IF(BA50<=$B$50,BA49,\"\")","v":""},{"$f":"IF(BB50<=$B$50,BB49,\"\")","v":""},{"$f":"IF(BC50<=$B$50,BC49,\"\")","v":""},{"$f":"IF(BD50<=$B$50,BD49,\"\")","v":""},{"$f":"IF(BE50<=$B$50,BE49,\"\")","v":""},{"$f":"IF(BF50<=$B$50,BF49,\"\")","v":""},{"$f":"IF(BG50<=$B$50,BG49,\"\")","v":""},{"$f":"IF(BH50<=$B$50,BH49,\"\")","v":""},{"$f":"IF(BI50<=$B$50,BI49,\"\")","v":""},{"$f":"IF(BJ50<=$B$50,BJ49,\"\")","v":""},{"$f":"IF(BK50<=$B$50,BK49,\"\")","v":""},{"$f":"IF(BL50<=$B$50,BL49,\"\")","v":""},{"$f":"IF(BM50<=$B$50,BM49,\"\")","v":""},{"$f":"IF(BN50<=$B$50,BN49,\"\")","v":""},{"$f":"IF(BO50<=$B$50,BO49,\"\")","v":""},{"$f":"IF(BP50<=$B$50,BP49,\"\")","v":""}]

{"sheet":"P&E(2)","index":4,"n_rows":30,"n_cols":7,"rows_kept":30,"cut":false,"hidden":false,"merged":[]}
["Web Site Visits"]
["# visits per minute",8]
["Time interval",1,"minute",60,"seconds"]
["Follows Poisson Probability Distribution"]
["Mean time Between Visits",null,"minutes"]
[]
["Poisson f(x)","f(x) = (μxe-μ)/x!","Hieght and probability"]
[null,{"$f":"\"f(x) = (\"&B2&\"^x * e^-\"&B2&\")/X!\"","v":"f(x) = (8^x * e^-8)/X!"}]
["where mew for Poisson ="]
[]
["Exponetial f(x)","f(x) = 1/μ*e-x/μ        For x >=0","Height"]
[null,{"$f":"\"f(x) = \"&1/B5&\" * e\"&\"^-(\"&1/B5&\"x)\"","v":{"$error":"#DIV/0!"}}]
[null,"P(x<=x0) = 1- e-x0/μ","Cumulative Prob",null,"X0 is upper end"]
[null,{"$f":"\"1 - e^-\"&1/B5&\"x0\"","v":{"$error":"#DIV/0!"}}]
["where mew for Exponential ="]
[]
["Poisson"]
["Mean =",{"$f":"B2","v":8}]
["x",0,null,null,null,"check"]
[{"$f":"\"P(x=\"&B19&\")\"","v":"P(x=0)"},null,null,null,null,{"$f":"(B18^B19*EXP(1)^-B18)/FACT(B19)","v":3.3546262790251196E-4},{"$f":"F20=B20","v":false}]
[]
["New Mean"]
["New Time Interval",25,"seconds"]
["x",0,null,null,null,"check"]
[{"$f":"\"P(x=\"&B24&\")\"","v":"P(x=0)"},null,null,null,null,{"$f":"(B22^B24*EXP(1)^-B22)/FACT(B24)","v":{"$error":"#NUM!"}},{"$f":"F25=B25","v":{"$error":"#NUM!"}}]
[]
["Exponential"]
["Mean",{"$f":"B3/B2","v":0.125},"Time (minutes) between visits"]
["x",{"$f":"1/4","v":0.25},"Time (minutes) between visits",null,null,"check"]
[{"$f":"\"P(x<=\"&B29&\")\"","v":"P(x<=0.25)"},null,null,null,null,{"$f":"1-EXP(1)^-(B29/B28)","v":0.8646647167633873},{"$f":"F30=B30","v":false}]

{"sheet":"P&E(2an)","index":5,"n_rows":30,"n_cols":7,"rows_kept":30,"cut":false,"hidden":false,"merged":[]}
["Web Site Visits"]
["# visits per minute",8]
["Time interval",1,"minute",60,"seconds"]
["Follows Poisson Probability Distribution"]
["Mean time Between Visits",{"$f":"B3/B2","v":0.125},"minutes"]
[]
["Poisson f(x)","f(x) = (μxe-μ)/x!","Hieght and probability"]
[null,{"$f":"\"f(x) = (\"&B2&\"^x * e^-\"&B2&\")/X!\"","v":"f(x) = (8^x * e^-8)/X!"}]
["where mew for Poisson =",{"$f":"B2","v":8}]
[]
["Exponetial f(x)","f(x) = 1/μ*e-x/μ        For x >=0","Height"]
[null,{"$f":"\"f(x) = \"&1/B5&\" * e\"&\"^-(\"&1/B5&\"x)\"","v":"f(x) = 8 * e^-(8x)"}]
[null,"P(x<=x0) = 1- e-x0/μ","Cumulative Prob",null,"X0 is upper end"]
[null,{"$f":"\"1 - e^-\"&1/B5&\"x0\"","v":"1 - e^-8x0"}]
["where mew for Exponential =",{"$f":"B5","v":0.125}]
[]
["Poisson"]
["Mean =",{"$f":"B2","v":8}]
["x",0,null,null,null,"check"]
[{"$f":"\"P(x=\"&B19&\")\"","v":"P(x=0)"},{"$f":"_xlfn.POISSON.DIST(B19,B18,0)","v":3.3546262790251185E-4},null,null,null,{"$f":"(B18^B19*EXP(1)^-B18)/FACT(B19)","v":3.3546262790251196E-4},{"$f":"F20=B20","v":true}]
[]
["New Mean",{"$f":"B23/60*B18","v":3.3333333333333335}]
["New Time Interval",25,"seconds"]
["x",0,null,null,null,"check"]
[{"$f":"\"P(x=\"&B24&\")\"","v":"P(x=0)"},{"$f":"_xlfn.POISSON.DIST(B24,B22,0)","v":3.5673993347252395E-2},null,null,null,{"$f":"(B22^B24*EXP(1)^-B22)/FACT(B24)","v":3.5673993347252388E-2},{"$f":"F25=B25","v":true}]
[]
["Exponential"]
["Mean",{"$f":"B3/B2","v":0.125},"Time (minutes) between visits"]
["x",{"$f":"1/4","v":0.25},"Time (minutes) between visits",null,null,"check"]
[{"$f":"\"P(x<=\"&B29&\")\"","v":"P(x<=0.25)"},{"$f":"_xlfn.EXPON.DIST(B29,1/B28,1)","v":0.8646647167633873},null,null,null,{"$f":"1-EXP(1)^-(B29/B28)","v":0.8646647167633873},{"$f":"F30=B30","v":true}]

{"sheet":"P&E3","index":6,"n_rows":15,"n_cols":4,"rows_kept":15,"cut":false,"hidden":false,"merged":[]}
[null,"interruptions at work",6]
[null,"Time interval",1,"hour"]
[]
[null,"New Mean",{"$f":"C1*C6","v":1.5},"# interuptions"]
[null,"New Time",15,"minutes"]
[null,"New Time",{"$f":"C5/60","v":0.25},"hours"]
[]
["b","Poisson"]
[null,"x",0,{"$f":"\"# interruptions per \"&C5&\" \"&D5","v":"# interruptions per 15 minutes"}]
[null,{"$f":"\"P(x=\"&C9&\")\"","v":"P(x=0)"},{"$f":"_xlfn.POISSON.DIST(C9,C4,0)","v":0.22313016014842982}]
[]
["c","Exponetial"]
[null,"Mean",{"$f":"C5/C4","v":10},"Time (minutes) between interuptions"]
[null,"x",10,"minutes between interuptions"]
[null,{"$f":"\"P(x<=\"&C14&\")\"","v":"P(x<=10)"},{"$f":"_xlfn.EXPON.DIST(C14,1/C13,1)","v":0.63212055882855767}]