HW4 - HW#4 Due 03/18 AMS 311 Probability Theory(Spring 2011...

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HW#4, Due 03/18 AMS 311 Probability Theory (Spring 2011) 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. Part 1 (10 points): PRINT your name and StonyBrook ID ( Last, First, #ID ) on the top on your work sheet. Staple your HW if more than 1 pages. Part 2: Problems (90 points) Write down your work step by step to get full score. (1). (10 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. (you need not evaluate any arithmetic expression) *** Please denote the events with letters clearly. (e.g., Let C be the event that the defendant is convicted (found to be guilty by at least 9 of the 12 jurors). Let G be the event that the defendant actually is guilty. Let E be the event that the jury renders a correct decision. The problem asks you to compute P(E).) (2). (10 points) A certain typing agency employs Alan, Bob, and Cathy as typists. The average number of errors per page is 3 when typed by Alan, 4.2 when typed by Bob, and 2.1 when typed
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HW4 - HW#4 Due 03/18 AMS 311 Probability Theory(Spring 2011...

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