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Unformatted text preview: (2) Let X n be the random variable that equals the number of tails minus the number of heads when n fair coins are Fipped. ind the expected value and the variance of X n . (3) Prove that log 2 (5) = 2 . 3219 ... is not a rational number. (4) Solve the recurrence relation a n = 6 a n-1-9 a n-2 with the initial conditions a = 1 and a 1 = 9. (5) A thumb tack is tossed until it rst lands with its point down, at which time no more tosses are made. On each tack toss, the probability of landing point down in 1 / 3. (a) ind the probability that exactly ve tosses are made. (b) What is the expected number of tosses?...
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- Spring '08