test5 - ¯ X(d Compute the probability ¯ X lies within.1...

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Fall 2008 Test V Page: 1 of 1 Introduction to Probability Monday, December 8, 2008 STA 4321/5325 Instructions: Please turn of your cell phones. Please write all oF your answers on a separate sheet oF paper and make sure you have clearly labeled the problem corresponding to your answer. Absolutely no cheating. This test has a total oF 60 points. Work as quickly and e±ciently as possible so that you can ²nish all oF the problems. Name: 1 (5*5=25 points) Let X 1 , . . . , X 36 iid exp(1). (a) Compute the pdf of the order statistic X ( n ) (max of the X ’s). (b) Compute the cdf of the order statistics X (2) (second smallest). (c) What is an approximate distribution for
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Unformatted text preview: ¯ X ? (d) Compute the probability ¯ X lies within .1 of the mean. (e) Compute a 95% con±dence interval for ¯ X . ◦ 2 (4*5=20 points) Let X ∼ unif(-1,1). (a) Compute the pdf of X . (b) Compute the cdf of Y = X 2 . (c) Compute the pdf of Y = X 2 . (d) Compute E[ X 2 ]. ◦ 3 (15 points) A soft-drink vending machine is set so that the amount of drink dispensed is a random variable with a mean of 200 milliliters and a standard deviation of 15 milliliters. What is the prob-ability that the average (mean) amount dispensed in a random sample of size 36 is at least 202 milliliters?...
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This note was uploaded on 10/04/2011 for the course STA 4321 taught by Professor Staff during the Fall '08 term at University of Florida.

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