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Unformatted text preview: Math136/Stat219 Fall 2009 Sample Final Examination Write your name and sign the Honor code in the blue books provided. You have 3 hours to solve all questions, each worth points as marked (maximum of 100). Complete reasoning is required for full credit. You may cite lecture notes and homework sets, as needed, stating precisely the result you use, why and how it applies. Important note: If you wish to use a result that is contained in an Exercise in the course notes that was not assigned for homework or proved in lecture, you must prove the result yourself (i.e. you cannot just site the Exercise number.) 1. (5x5) Consider a simple, symmetric random walk. That is, let ξ 1 , ξ 2 , . . . be a sequence of independent random variables with P ( ξ k = 1) = P ( ξ k = 1) = 1 / 2 for all k . Let S = 0 and S n = ∑ n k =1 ξ k for n = 1 , 2 , . . . . Let F n = σ ( ξ 1 , . . . , ξ n ). For fixed positive integers a and b let τ = min { n ≥ 0 : S n / ∈ ( a, b ) } . You may assume that τ < ∞ a.s....
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 Spring '09
 Math, Brownian Motion, Probability theory, Stochastic process, Yt

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