STAT 333 a2

STAT 333 a2 - Stat 333 - Assignment 2 - Fall 2011 Due...

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Unformatted text preview: Stat 333 - Assignment 2 - Fall 2011 Due Thursday November 10 at the beginning of class 1. Consider repeated Bernoulli trials, each with a probability of success P ( S ) = p . Let e n = Pr(even number of S s in n trials). Assume zero is even. (a) Show that e n = q e n- 1 + p (1- e n- 1 ) , n 1 . (b) Hence, find the probability generating function of { e n } n . (c) Let p = 0 . 5 . Find an explicit expression for e n , n . 2. Prove the Delayed Renewal Relation. (Hint: the proof is very similar to that of the Re- newal Relation, and you have to be very careful with the starting values of sums.) 3. Javids world-class cricketing career has recently begun. In a single game of cricket, he is said to score a century if he scores at least 100 runs. The number of matches until he scores a century has a Geometric (0 . 01) distribution. (a) Let be the event that he scores a century in a game....
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STAT 333 a2 - Stat 333 - Assignment 2 - Fall 2011 Due...

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