Understanding Coin Toss Outcomes: Continuous vs Discrete Payoffs

School

McMaster University**We aren't endorsed by this school

Course

COMMERCE 2DA3

Subject

Accounting

Date

Dec 10, 2024

Pages

Uploaded by KidReindeerPerson1256

Coin Toss ExampleSolution 1- Continuous UniformSolution 2- Discrete UniformReplicationsRand #E PayoffAvg PayoffE Payoff (D)Avg Payoff (D)10.214324100100110010020.546577050110010030.18448910066.66666667110010040.15158810075007550.392041008011008060.47263510083.33333333110083.33333333370.34053910085.714285710071.42857142980.93223607511007590.35301810077.77777778110077.777777778100.348064100800070110.44779110081.81818182110072.727272727120.08145410083.33333333110075130.39144910084.61538462110076.923076923140.702453078.571428570071.428571429150.116069100800066.666666667160.663742075110068.75170.793143070.588235290064.705882353180.985772066.666666670061.111111111190.35670310068.421052630057.894736842200.249085100700055210.818006066.66666667110057.142857143220.2282310068.181818180054.545454545230.46153110069.56521739110056.52173913240.46739510070.83333333110058.333333333250.854782068110060260.693948065.38461538110061.538461538270.890381062.962962960059.259259259280.863861060.71428571110060.714285714290.06107410062.06896552110062.068965517300.08721210063.333333330060310.515566061.290322580058.064516129320.14814410062.50056.25330.517437060.606060610054.545454545340.695021058.823529410052.941176471350.550677057.14285714110054.285714286360.14142510058.333333330052.777777778370.00120110059.45945946110054.054054054380.24221410060.526315790052.631578947390.28144310061.538461540051.282051282400.7550920600050Rand # (Discrete)

410.66879058.53658537110051.219512195420.637356057.142857140050430.749561055.81395349110051.162790698440.83687054.545454550050450.10958110055.55555556110051.111111111460.74464054.34782609110052.173913043470.24170210055.31914894110053.191489362480.91961054.16666667110054.166666667490.25892910055.102040820053.06122449500.85158054110054510.910131052.941176470052.941176471520.17273410053.84615385110053.846153846530.30198210054.716981130052.830188679540.34034510055.55555556110053.703703704550.988315054.545454550052.727272727560.161810055.35714286110053.571428571570.681968054.38596491110054.385964912580.25663410055.17241379110055.172413793590.674702054.237288140054.237288136600.365151100550053.333333333610.745153054.098360660052.459016393620.655478053.22580645110053.225806452630.723488052.38095238110053.968253968640.14051310053.1250053.125650.20777710053.84615385110053.846153846660.35653710054.545454550053.03030303670.04378610055.22388060052.23880597680.33281310055.882352940051.470588235690.09462910056.52173913110052.173913043700.678055.714285710051.428571429710.956881054.929577460050.704225352720.909343054.166666670050730.47793710054.79452055110050.684931507740.2832910055.405405410050750.543916054.666666670049.333333333760.22963710055.26315789110050770.13859810055.84415584110050.649350649780.556046055.12820513110051.282051282790.17917910055.69620253110051.898734177800.805354055110052.5810.07360110055.55555556110053.086419753820.569573054.878048780052.43902439830.704317054.21686747110053.012048193840.583218053.57142857110053.571428571850.3840910054.117647060052.941176471

860.3800710054.651162790052.325581395870.557654054.022988510051.724137931880.825507053.40909091110052.272727273890.869254052.80898876110052.808988764900.621311052.222222220052.222222222910.688582051.64835165110052.747252747920.26582910052.17391304110053.260869565930.625444051.612903230052.688172043940.44307410052.12765957110053.191489362950.783754051.57894737110053.684210526960.960229051.041666670053.125970.592538050.515463920052.577319588980.05736710051.020408160052.040816327990.2188410051.515151520051.5151515151000.80848705100511010.868356050.49504950050.4950495051020.891426050110050.9803921571030.06567610050.485436890050.4854368931040.62373305000501050.12056210050.47619048110050.4761904761060.67303305000501070.635524049.532710280049.532710281080.756822049.074074071100501090.19941710049.54128440049.5412844041100.12008100501100501110.877289049.54954955110050.450450451120.36862710050110050.8928571431130.912738049.557522120050.4424778761140.847209049.12280702110050.8771929821150.528352048.695652170050.4347826091160.705968048.27586207110050.8620689661170.41228410048.71794872110051.2820512821180.886469048.30508475110051.6949152541190.740751047.899159660051.2605042021200.47631510048.333333330050.8333333331210.45608610048.760330580050.413223141220.681814048.36065574110050.8196721311230.820068047.96747967110051.2195121951240.12225710048.387096770050.8064516131250.6993580480050.41260.743842047.61904762110050.7936507941270.69733047.24409449110051.1811023621280.12432810047.656250050.781251290.859738047.28682171110051.1627906981300.25803910047.69230769110051.538461538

1310.29579610048.091603050051.1450381681320.19545710048.48484848110051.5151515151330.92157048.12030075110051.8796992481340.23150410048.50746269110052.238805971350.712993048.14814815110052.5925925931360.617102047.794117650052.2058823531370.2192310048.17518248110052.5547445261380.19365410048.550724640052.1739130431390.06559210048.92086331110052.5179856121400.902216048.57142857110052.8571428571410.566134048.22695035110053.1914893621420.03033810048.5915493110053.5211267611430.535665048.251748250053.1468531471440.988965047.916666670052.7777777781450.16611810048.275862070052.4137931031460.73549047.945205480052.0547945211470.633999047.619047620051.7006802721480.543456047.29729730051.3513513511490.937447046.979865770051.0067114091500.06451510047.333333330050.6666666671510.02816110047.68211921110050.9933774831520.974993047.36842105110051.3157894741530.12712310047.71241830050.9803921571540.678269047.4025974110051.2987012991550.36211410047.74193548110051.6129032261560.631326047.43589744110051.9230769231570.544156047.13375796110052.2292993631580.30724710047.46835443110052.531645571590.656208047.16981132110052.8301886791600.520151046.8750052.51610.05692910047.20496894110052.7950310561620.19941410047.5308642110053.0864197531630.871021047.23926380052.7607361961640.618225046.95121951110053.0487804881650.0453710047.272727270052.7272727271660.848554046.987951810052.4096385541670.67043046.706586830052.0958083831680.35853710047.02380952110052.3809523811690.41073210047.33727811110052.6627218931700.726262047.058823530052.3529411761710.07378710047.36842105110052.6315789471720.31791110047.6744186110052.9069767441730.696991047.398843930052.6011560691740.37413410047.70114943110052.8735632181750.652801047.428571430052.571428571

1760.761703047.15909091110052.8409090911770.859625046.89265537110053.1073446331780.911255046.629213480052.8089887641790.32581810046.9273743110053.0726256981800.60115046.666666670052.7777777781810.915371046.408839780052.4861878451820.37850510046.70329670052.1978021981830.28033710046.99453552110052.4590163931840.660686046.73913043110052.7173913041850.07335210047.02702703110052.9729729731860.823307046.774193550052.6881720431870.514141046.52406417110052.9411764711880.23820910046.80851064110053.1914893621890.17383310047.089947090052.910052911900.3727810047.36842105110053.1578947371910.18763310047.643979060052.8795811521920.05960910047.916666670052.6041666671930.16265410048.1865285110052.8497409331940.859081047.938144330052.5773195881950.648799047.692307690052.3076923081960.04411710047.959183670052.0408163271970.47025810048.223350250051.7766497461980.761026047.979797980051.5151515151990.692861047.73869347110051.758793972000.153765100481100522010.08192910048.258706470051.7412935322020.46100810048.51485149110051.980198022030.17150210048.76847291110052.2167487682040.822925048.52941176110052.4509803922050.607422048.292682930052.1951219512060.23053710048.54368932110052.4271844662070.919812048.309178740052.1739130432080.23413110048.557692310051.9230769232090.41394110048.803827750051.6746411482100.906333048.571428570051.4285714292110.868976048.341232230051.1848341232120.698202048.11320755110051.415094342130.756786047.887323940051.173708922140.728413047.66355140050.9345794392150.07231910047.90697674110051.1627906982160.31902110048.148148150050.9259259262170.792722047.926267280050.691244242180.47793210048.16513761110050.9174311932190.783043047.94520548110051.1415525112200.894621047.727272730050.909090909

2210.07872910047.96380090050.6787330322220.646764047.747747750050.450450452230.871055047.53363229110050.672645742240.795568047.32142857110050.8928571432250.836677047.111111110050.6666666672260.34477410047.34513274110050.8849557522270.38440510047.57709251110051.1013215862280.32975910047.807017540050.8771929822290.701334047.598253280050.6550218342300.18026510047.82608696110050.8695652172310.24923610048.05194805110051.0822510822320.695558047.84482759110051.2931034482330.863419047.63948498110051.5021459232340.3963510047.863247860051.2820512822350.0843910048.08510638110051.4893617022360.38096710048.30508475110051.6949152542370.05495910048.523206750051.4767932492380.36108210048.7394958110051.6806722692390.32248910048.95397490051.4644351462400.19825910049.166666670051.252410.38567810049.377593360051.0373443982420.15005710049.586776860050.8264462812430.733422049.38271605110051.0288065842440.68645049.180327870050.8196721312450.38982810049.38775510050.6122448982460.875747049.18699187110050.813008132470.37649210049.392712550050.6072874492480.47588310049.596774190050.4032258062490.28769410049.799196790050.2008032132500.4489271005000502510.949851049.800796810049.8007968132520.612861049.60317460049.6031746032530.737005049.407114620049.4071146252540.7202049.212598430049.2125984252550.21041810049.41176471110049.4117647062560.0315710049.6093750049.218752570.821347049.416342410049.0272373542580.33589110049.61240310048.8372093022590.43781110049.80694981110049.0347490352600.652814049.615384620048.8461538462610.28163110049.808429120048.6590038312620.535355049.618320610048.4732824432630.735198049.429657790048.2889733842640.07054210049.621212120048.1060606062650.71907049.433962260047.924528302

2660.20465510049.62406015110048.1203007522670.557093049.438202250047.9400749062680.96209049.25373134110048.1343283582690.06492710049.442379180047.9553903352700.914714049.259259260047.7777777782710.3186410049.44649446110047.9704797052720.924573049.264705880047.7941176472730.3190110049.45054945110047.9853479852740.33125510049.6350365110048.1751824822750.04162110049.8181818200482760.24636210050110048.1884057972770.24882510050.18050542110048.3754512642780.05153810050.35971223110048.5611510792790.83347050.179211470048.3870967742800.9608250500048.2142857142810.44603410050.17793594110048.3985765122820.46658610050.354609930048.2269503552830.33880410050.530035340048.0565371022840.08473110050.70422535110048.239436622850.739476050.526315790048.0701754392860.933273050.34965035110048.2517482522870.903553050.17421603110048.4320557492880.39982410050.347222220048.2638888892890.628171050.173010380048.0968858132900.41166310050.344827590047.9310344832910.89498050.17182131110048.1099656362920.5448060500047.9452054792930.576722049.829351540047.7815699662940.961855049.65986395110047.9591836732950.18285610049.83050847110048.135593222960.659671049.662162160047.9729729732970.632808049.49494949110048.1481481482980.596298049.328859060047.9865771812990.644369049.1638796110048.1605351173000.07486110049.33333333110048.3333333333010.569011049.16943522110048.5049833893020.948731049.006622520048.3443708613030.35315110049.17491749110048.5148514853040.15706610049.34210526110048.6842105263050.25276510049.50819672110048.8524590163060.48804410049.673202610048.6928104583070.3226710049.83713355110048.8599348533080.953304049.67532468110049.0259740263090.877701049.51456311110049.1909385113100.23174510049.677419350049.032258065

3110.732012049.517684890048.8745980713120.902359049.358974360048.7179487183130.583714049.20127796110048.8817891373140.38649310049.36305732110049.0445859873150.986706049.20634921110049.2063492063160.28540710049.36708861110049.3670886083170.12856510049.526813880049.2113564673180.510342049.371069180049.0566037743190.710848049.21630094110049.216300943200.20548210049.375110049.3753210.703406049.22118380049.2211838013220.01177810049.378881990049.0683229813230.881642049.226006190048.9164086693240.810856049.074074070048.7654320993250.689314048.923076920048.6153846153260.4757110049.07975460048.4662576693270.564188048.929663610048.3180428133280.26250610049.085365850048.1707317073290.809084048.936170210048.0243161093300.959914048.78787879110048.1818181823310.735324048.64048338110048.338368583320.603616048.4939759110048.4939759043330.11783710048.64864865110048.6486486493340.19664310048.802395210048.5029940123350.25857610048.95522388110048.6567164183360.19976710049.10714286110048.809523813370.13519210049.258160240048.6646884273380.37248210049.408284020048.5207100593390.728846049.26253687110048.6725663723400.553184049.11764706110048.8235294123410.35328910049.26686217110048.9736070383420.34843110049.41520468110049.1228070183430.906121049.27113703110049.2711370263440.501114049.127906980049.1279069773450.7674048.98550725110049.2753623193460.42026910049.13294798110049.4219653183470.33083710049.2795389110049.5677233433480.30265410049.42528736110049.7126436783490.999295049.283667620049.5702005733500.831128049.14285714110049.7142857143510.943633049.002849110049.8575498583520.742101048.863636361100503530.18162710049.00849858110050.1416430593540.31193510049.1525423700503550.609501049.014084510049.85915493

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8960.804549050.558035710048.9955357148970.981594050.50167224110049.0523968788980.10363510050.55679287110049.1091314038990.77252050.50055617110049.1657397119000.25526810050.555555560049.1111111119010.4128810050.610432850049.0566037749020.601874050.55432373110049.113082049030.885124050.49833887110049.1694352169040.777592050.442477880049.1150442489050.709032050.386740330049.0607734819060.961794050.331125830049.0066225179070.09758410050.385887540048.9525909599080.449510050.44052863110049.0088105739090.47752510050.49504950048.954895499100.17165510050.54945055110049.0109890119110.666385050.493962680048.9571899019120.520379050.43859649110049.0131578959130.870162050.38335159110049.0690032869140.905963050.328227570049.0153172879150.43764310050.382513660048.9617486349160.37240510050.43668122110049.0174672499170.693428050.38167939110049.073064349180.3740110050.43572985110049.1285403059190.819502050.38084875110049.1838955399200.96481050.326086960049.1304347839210.640535050.27144408110049.1856677529220.783687050.21691974110049.2407809119230.918148050.16251354110049.2957746489240.35369810050.21645022110049.3506493519250.98136050.162162160049.2972972979260.49664110050.215982720049.2440604759270.45874610050.269687160049.1909385119280.645172050.215517240049.1379310349290.632089050.161463940049.0850376759300.66807050.10752688110049.1397849469310.2972410050.16111708110049.1944146089320.665197050.10729614110049.2489270399330.430210050.1607717110049.3033226159340.2121410050.21413276110049.3576017139350.24569410050.26737968110049.4117647069360.74395050.21367521110049.4658119669370.16584910050.26680896110049.5197438639380.01605210050.31982942110049.5735607689390.911541050.26624068110049.6272630469400.48556410050.319148940049.574468085

9410.49853410050.371944740049.5217853359420.697274050.31847134110049.575371559430.07523310050.37115589110049.6288441159440.47122910050.42372881110049.682203399450.652408050.37037037110049.7354497359460.936585050.31712474110049.788583519470.04748810050.369588170049.7360084489480.767612050.3164557110049.7890295369490.28883210050.368809270049.7365648059500.43593410050.421052630049.6842105269510.22544910050.47318612110049.7371188229520.547156050.420168070049.684873959530.23632510050.47219307110049.7376705149540.42843710050.52410901110049.7903563949550.12143510050.57591623110049.8429319379560.903998050.523012550049.7907949799570.36503310050.574712640049.738766989580.32087810050.6263048110049.7912317339590.23105410050.677789360049.7393117839600.760187050.625110049.7916666679610.601678050.57232050049.7398543189620.970942050.519750520049.6881496889630.627397050.46728972110049.74039469640.744886050.414937760049.688796689650.877331050.3626943110049.7409326429660.46747710050.41407867110049.7929606639670.38820110050.46535677110049.8448810759680.754448050.41322314110049.8966942159690.24085210050.464396280049.8452012389700.935445050.41237113110049.8969072169710.12168910050.463439750049.8455200829720.896792050.41152263110049.8971193429730.25539110050.462487150049.8458376169740.689726050.410677620049.7946611919750.879749050.358974360049.7435897449760.897045050.307377050049.6926229519770.28864810050.35823951110049.7441146379780.46769410050.40899796110049.7955010229790.802146050.357507660049.7446373859800.16389610050.40816327110049.7959183679810.790065050.3567788110049.8470948019820.03992510050.407331980049.7963340129830.33897310050.45778230049.7456765019840.563048050.40650407110049.7967479679850.95161050.35532995110049.847715736

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1000 ReplicationsPayoff5010050.249.6505050505050505050505050505050505050505050505050505050505050505050505050505050Closed-formAvg PayoffAvg Payoff (D)155 109163217271325379433487541595649703757811865919973020406080100120Chart TitleAvg CAvg DClosed form

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