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Stat 5131 (Geyer) Old Final Exam

Stat 5131 (Geyer) Old Final Exam - Let X be the time until...

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Up: Stat 5131 Stat 5131 Final Exam, December 11, 1997 Problem 1 A gambler makes 100 one-dollar bets on red at roulette. The probability of winning a single bet is 18 / 38. The bets pay even odds, so the gambler gains $1 when he wins and loses $1 when he loses. What is the mean and the standard deviation of the gambler's net gain (amount won minus amount lost) on the 100 bets? Problem 2 A die is rolled 200 times. What is the probability that the number of sixes rolled is greater than or equal to 40? Use the normal approximation with continuity correction to calculate this. Problem 3 I arrive at a bank. There is one teller. Four customers are in line in front of me. Assume that customer service times are independent and exponentially distributed with mean service time five minutes.
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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 1998-09-25...
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