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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Counting your moneyCLT and<strong>Random</strong><strong>Walk</strong>JeffreySchenkerA GameWorking onthe ProblemInterlude:Gambler’sRuinCLTRand. <strong>Walk</strong><strong>Brownian</strong><strong>Motion</strong>How big is W n =n∑j=1w j ?Average winnings: Av(W n ) = ∑ n j=1 Av(w j) = 0.Doesn’t say how big W n is.Average square Av(Wn 2 ) = ∑Av(w i w j ) = n.i,jAv(w i w j ) = 0 if i ̸= jAv(w 2i) = 1
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