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Unformatted text preview: wins the match. Each game is won by Fischer with probability p, by Spassky with probability q, and is a draw with probability 1-p-q . What is the probability that Fischer wins the match? What is the PMF, the mean, and the variance of the duration of the match? Problem 4 You are visiting the rainforest, but unfortunately your insect repellent has run out. As a result, at each second, a mosquito lands on your neck with probability 0.4. If a mosquito lands, it will bite you with probability 0.4, and it will never bother you with probability 0.6, independently of other mosquitoes. What is the expected time between successive bites? Problem 5 Let X 1 ,...,X n be independent, identically distributed random variables with common mean and variance. Find the values of c and d that will make the following formula true: E [( X 1 + .... + X n ) 2 ] = cE [ X 2 1 ] + d ( E [ X 1 ]) 2 ....
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- Spring '10