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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Chebyshev’s InequalityCLT and<strong>Random</strong><strong>Walk</strong>JeffreySchenkerA GameWorking onthe ProblemInterlude:Gambler’sRuinCLTRand. <strong>Walk</strong><strong>Brownian</strong><strong>Motion</strong>n = Av(Wn 2 n) = ∑ m 2 Prob(W n = m)m=−n≥ 100Prob(W 10 = 10)Prob(W n = 10) ≤n100 ,The probability of winning in exactly n steps is no largerthan n/100.