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Math511ReviewProblemsExam2

# Example the permutation 2 6 1 5 9 3 7 4 8 of the

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Unformatted text preview: required. What is the expected value of X? Examples: 4 5 3 6 6 6 6 4 OR 2 2 5 4 3 1 6 6 6 6 6 3 OR 62. 13. (a). Suppose that each box of corn flakes contains one of eight different action figures as prizes. What is the expected number of boxes you must buy to collect three different prizes? (b). Suppose that each box of corn flakes contains one of 20 different action figures as prizes. What is the expected number of distinct prizes you will get if you buy 20 boxes? Approximate your answer in terms of e. Hint: Let X denote the number of distinct prizes obtained. Then we can express X in terms of indicator random variables by X = X1 + X2 + X 3 + X20 where, X k = 1 ⇔ we get prize k and X k = 0 otherwise. 14. Suppose that X is a geometric random variable and P( X < 2) = 1 , what is the value of 25 P( X ≥ 4 ) ? 15. Suppose that X and Y are random variables where X is a Poisson random variable with mean 3 and Y is a binomial random variable that is b (20, 0...
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