Question: Stat 333 - Assignment 2 Question 1 1. Suppose we continue to randomly select letters with replacement from the set {A, B, C, D}. Let

Stat 333 - Assignment 2 Question 1

Stat 333 - Assignment 2 Question 1 1. Suppose we continue to

1. Suppose we continue to randomly select letters with replacement from the set {A, B, C, D}. Let T = be the number of letters we need to collect in order to have both letter A and letter B at least once. For example, suppose we have a sequence of letters CCADABB . ... Then T =6 in the above sequence. (a) Find the probability generating function of T and use it to find P(T = n) for n 2 1. (b) Use the probability generating function of T to find E(T) and Var(T). Hint: T can be expressed as the summation of two independent rvs

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