Central Limit Theorem, Random Walk, Brownian Motion

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OutlineCLT andRandomWalkJeffreySchenkerA GameWorking onthe ProblemInterlude:Gambler’sRuinCLTRand. WalkBrownianMotion1 Prelude: A Simple Game2 Working on the Problem3 Interlude: Gambler’s Ruin4 Central Limit Theorem5 Random Walk6 Brownian Motion
We want to WIN!CLT andRandomWalkJeffreySchenkerA GameWorking onthe ProblemInterlude:Gambler’sRuinCLTRand. WalkBrownianMotionWe don’t care how long it takes, we just want towin!Setup:your initial fortune: f.your target fortune: BP(f)=probability that you make your target beforeyou lose everything.Fundamental identity:P(f ) = 1 2(P(f + 1) + P(f − 1))P(0) = 0P(B) = 1Solution: P(f )= f B .
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 13 and 14: OutlineCLT andRandomWalkJeffreySche
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 and 22: Gambler’s RuinCLT andRandomWalkJe
Page 23 and 24: How quickly can you win?CLT andRand
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

Central Limit Theorem, Random Walk, Brownian Motion

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