Unformatted text preview: probabilities p, 1p , in other words S n = X 1 + ··· + X n and the { X i } are i.i.d. random variables with distribution P ( X i = 1) = p and P ( X i =1) = 1p. Fix a positive integer b > 0, and let T be the ﬁrst hitting time of the point b : T ( ω ) = inf { n ≥ 1 : S n ( ω ) = b } . If the walk never hits b , in other words the set { n : S n ( ω ) = b } is empty, then T ( ω ) = ∞ . Calculate the expectation ET . Be sure to justify everything....
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This note was uploaded on 11/18/2009 for the course MATH 241 taught by Professor Reed during the Spring '09 term at Duke.
 Spring '09
 Reed
 Probability

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