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hw4 - AMS 311(Fall 2010 Joe Mitchell PROBABILITY THEORY...

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AMS 311 (Fall, 2010) Joe Mitchell PROBABILITY THEORY Homework Set # 4 Due at the beginning of class on Thursday, October 21, 2010. Reminder: Show your reasoning! Read: Ross, Chapter 4, Sections 4.5–4.9 (you can skip the Hypergeometric distribution (4.8.3) and the Zeta distribution (4.8.4)), Sections 5.1–5.3. SUBMIT ANY 4 OF THE 8 PROBLEMS BELOW. You should read and understand how to do all 8 of them. (1). (25 points) The cdf of X is given by F ( x ) = 0 x < 4 3 / 10 4 x < 1 7 / 10 1 x < 4 1 x 4 (a). (10 points) Find the variance and the standard deviation of X . (b). (5 points) Find the variance of Y = X 3 + 12. (c). (10 points) Find the cdf of W = 2 X 2 3. (2). (25 points) Suppose it takes at least 9 votes from a 12-member jury to convict a defendant. Suppose the probability that a juror votes a guilty person innocent is 0.2, whereas the probability that the juror votes an innocent person guilty is 0.1. If each juror acts independently and if 65 percent of the defendants are guilty, find the probability that the jury renders a correct decision.

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hw4 - AMS 311(Fall 2010 Joe Mitchell PROBABILITY THEORY...

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