Central Limit Theorem, Random Walk, Brownian Motion
Central Limit Theorem, Random Walk, Brownian Motion
Central Limit Theorem, Random Walk, Brownian Motion
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How quickly can you win?CLT and<strong>Random</strong><strong>Walk</strong>JeffreySchenkerA GameWorking onthe ProblemInterlude:Gambler’sRuinCLTRand. <strong>Walk</strong><strong>Brownian</strong><strong>Motion</strong>It 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 =
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