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midterm 2

# midterm 2 - (2 Let X n be the random variable that equals...

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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 ²rst 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 ²ve tosses are made. (b) What is the expected number of tosses?...
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