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Unformatted text preview: X 1 and X 2 ? Both X 1 and X 2 are geometric with parameter 1 / 6. b) What is the probability that they tie? (Hint: you may want write this in terms of the X ’s and use conditioning) This is a simpliﬁed version of the hw #3, Pb 63 problem. Have to ﬁnd the probability P ( X 1 = X 2 ), that we get by conditioning, or equivalently by considering all possible values for X 1 and X 2 : P ( X 1 = X 2 ) = ∞ X 1= i P ( X 1 = X 2 = i ) = ∞ X 1= i 1 / 6(5 / 6) i1 1 / 6(5 / 6) i1 = 1 / 36 ∞ X 1= i (25 / 36) i1 = 1 36 1 125 / 36 = 1 / 11 c) What is the probability that John wins? By symmetry, 1 = P (John wins)+ P (Mary wins)+ P (they tie) = 2 P (John wins)+ P (they tie). So by a) we get that P (John wins) = 5 / 11...
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This note was uploaded on 10/02/2009 for the course PSTAT 5E taught by Professor Eduardomontoya during the Spring '08 term at UCSB.
 Spring '08
 EduardoMontoya

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