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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Setting up the problem.CLT and<strong>Random</strong><strong>Walk</strong>JeffreySchenkerA GameWorking onthe ProblemInterlude:Gambler’sRuinCLTRand. <strong>Walk</strong><strong>Brownian</strong><strong>Motion</strong>Let w i = your winnings in i th round of the game.w i is a random variable:{$1 if the i th coin flip is tails,w i =−$1 if the i th coin flip is heads.w i and w j for different coin tosses areindependent.Your winnings after playing the game n times:W n = w 1 + w 2 + · · · + w n =n∑ w j .j=1
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