hw4 - AMS 311 (Fall, 2009) Joe Mitchell PROBABILITY THEORY...

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Unformatted text preview: AMS 311 (Fall, 2009) Joe Mitchell PROBABILITY THEORY Homework Set # 4 Due at the beginning of class on Thursday, October 22, 2009. Reminder: Show your reasoning! Read: Ross, Chapter 4, Sections 4.54.10 (you can skip the Hypergeometric distribution (4.8.3) and the Zeta distribution (4.8.4)), Sections 5.15.3. SUBMIT SOLUTIONS TO 4 OF THE 7 PROBLEMS BELOW, INCLUDING (at least) ONE OF PROBLEMS 6 AND 7. You are responsible to be able to solve all 7 of them. (1). (25 points) The cdf of X is given by F ( x ) = x <- 4 3 / 10- 4 x < 1 7 / 10 1 x < 4 1 x 4 (a). (15 points) Find the variance and the standard deviation of X . (b). (10 points) Find the variance of Y = 3 p ( X ) + P ( X > 2), where p ( ) is the pmf of X . (2). (25 points) Problem 4.46, Ross 8th edition (it is problem 46, page 193, Ross 7th edition). I will help you set up the problem (though you should be able to do this!). Let C be the event that the defendent is convicted (found to be guilty by at least 9 of the 12 jurors). Letthe defendent is convicted (found to be guilty by at least 9 of the 12 jurors)....
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