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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Eureka?CLT and<strong>Random</strong><strong>Walk</strong>JeffreySchenkerA GameWorking onthe ProblemInterlude:Gambler’sRuinCLTRand. <strong>Walk</strong><strong>Brownian</strong><strong>Motion</strong>So, as long as we don’t choose B too large, sof /B > 1/2, we have a better than even chance ofmaking our goal! Let’s go to the Casino!Wait a minute.... What are our expected winnings?With probability f /B we win B − f dollars.With probability 1 − f /B we lose f dollars.Expected winnings(B − f ) f (B − f 1 − f )= 0!B
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