Central Limit Theorem, Random Walk, Brownian Motion

More documents

Recommendations

Info

Gambler’s RuinCLT andRandomWalkJeffreySchenkerRemember, we each start with $10.A GameWorking onthe ProblemInterlude:Gambler’sRuinCLTRand. WalkBrownianMotionThe game stops when your total winnings W nreach either$10 (you win all my money)or −$10 (I win all your money)But, will the game always reach an end?How can we tell?
How quickly can you win?CLT andRandomWalkJeffreySchenkerA GameWorking onthe ProblemInterlude:Gambler’sRuinCLTRand. WalkBrownianMotionIt is impossible for me to win in less then 10 plays.It is possible for me to win after 10 plays, but prettyunlikely:Prob(W 10 = 10) = probability of 10 straight tails= 1 = 12 10 1024 ≈ 0.00098What about within 11 plays?What about 12 plays?Prob(W 10 = 10 or W 12 = 10) = 171024 ≈ 0.0068Still pretty unlikely!1024 + 101024 × 1 4 =
Page 2 and 3: OutlineCLT andRandomWalkJeffreySche
Page 4 and 5: A fair game.CLT andRandomWalkJeffre
Page 6 and 7: A fair game.CLT andRandomWalkJeffre
Page 8: How long can we play?CLT andRandomW
Page 11 and 12: How long can we play?CLT andRandomW
Page 15 and 16: Setting up the problem.CLT andRando
Page 17 and 18: Setting up the problem.CLT andRando
Page 19 and 20: Gambler’s RuinCLT andRandomWalkJe
Page 21: Gambler’s RuinCLT andRandomWalkJe
Page 25 and 26: How quickly can you win?CLT andRand
Page 28 and 29: Counting your moneyCLT andRandomWal
Page 30 and 31: Counting your moneyCLT andRandomWal
Page 32 and 33: Chebyshev’s InequalityCLT andRand
Page 34 and 35: Chebyshev’s InequalityCLT andRand
Page 36 and 37: Kolomogorov’s InequalityCLT andRa
Page 38 and 39: Averages can be misleading:CLT andR
Page 43 and 44: We want to WIN!CLT andRandomWalkJef
Page 45 and 46: Eureka?CLT andRandomWalkJeffreySche
Page 47 and 48: Moment generating functionCLT andRa
Page 49 and 50: Stands 17-18SM EdicionesMagdalena n
Page 52 and 53: Computing the MGFCLT andRandomWalkJ
Page 54 and 55: Computing the MGFCLT andRandomWalkJ
Page 56: Módulo (D)Escuela de Escritores de
Page 59 and 60: Central LimitCLT andRandomWalkJeffr
Page 61 and 62: The Bell CurveCLT andRandomWalkJeff
Page 63 and 64: Central Limit TheoremCLT andRandomW
Page 65 and 66: Central Limit TheoremCLT andRandomW
Page 67 and 68: Drunkards WalkCLT andRandomWalkJeff
Page 69 and 70: Central Limit Theorem V2.0CLT andRa
Page 71 and 72: BrownCLT andRandomWalkJeffreySchenk
Page 73 and 74:
BrownCLT andRandomWalkJeffreySchenk
Page 75 and 76:
Einstein’s ExplanationCLT andRand
Page 77 and 78:
Einstein’s ExplanationCLT andRand
show all

Central Limit Theorem, Random Walk, Brownian Motion

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?