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midterm 2002 - the probability that exactly 15 couples must...

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Statistics 116 Midterm Examination - July 22, 2002 - 9:OOam NAME: Show all work! Justify your assertions! 1 . There are 3 coins in a box. One is two-headed, another is a fair coin, and the third is a biased coin that comes up heads 75 percent of the time. When one of the 3 coins is selected at random and flipped, it shows heads. What is the probability that it was the two-headed coin? (20 points) 2. A pediatrician wishes to recruit 5 couples, each of which is expecting their first child, to participate in a new natural childbirth regimen. If p = .2 is the probability that a randomly selected couple agrees to participate, what is
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Unformatted text preview: the probability that exactly 15 couples must be asked before 5 are found who agree to participate? (20) 3. It is known that Peter can beat James at chess with probability .6. What is the probability that Peter wins 4 games before James wins 4 games? (20) 4. Suppose X is uniform on [- 1, 1 1. Find a. the density function of the random variable I 3X 1. b. the variance of I 3X I 5. Given 30 people at a party, find the probability that among the 12 months of the year, there are 6 containing exactly 2 birthdays and 6 containing exactly 3. (20)...
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