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Unformatted text preview: Let X be the time until I get out of the bank (that is, all five customers including me have been served). a. Find the mean of X . b. Find the standard deviation of X . c. Find the probability that X is less than a half hour. Problem 4 Suppose . Let Y = 1 / X . a. For which values of and does E ( Y ) exist? b. What is E ( Y ) when it exists? Problem 5 If X , Y , and Z are independent random variables, what is P ( X > Y + Z )? Hint: What is the distribution of X Y Z ? Problem 6 A pair of random variables X and Y have joint p. d. f. Find the conditional p. d. f. of X given Y . Problem 7 The conditional p. d. f. of X given Y is Find the regression function of X on Y . Problem 8 Suppose . What is the p. d. f. of Y = 1 / X ? Up: Stat 5131 Charles Geyer 19980925...
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 Spring '02
 Staff
 Probability

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