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Unformatted text preview: ime they will stay is exponentially distributed with means of
1, 1/2, and 1/3 hour. (a) What is the expected time until only one student
remains? (b) For each student ﬁnd the probability they are the last student
left. (c) What is the expected time until all three students are gone?
2.17. Let Ti , i = 1, 2, 3 be independent exponentials with rate
that for any numbers t1 , t2 , t3
max{t1 , t2 , t3 } = t1 + t2 + t3 min{t1 , t2 } min{t2 , t3 } + min{t1 , t2 , t3 } i. (a) Show min{t1 , t3 } (b) Use (a) to ﬁnd E max{T1 , T2 , T3 }. (c) Use the formula to give a simple
solution of part (c) of Exercise 2.16.
Poisson approximation to binomial
2.18. Compare the Poisson approximation with the exact binomial probabilities
of 1 success when n = 20, p = 0.1.
2.19. Compare the Poisson approximation with the exact binomial probabilities
of no success when (a) n = 10, p = 0.1, (b) n = 50, p = 0.02.
2.20. The probability of a three of a kind in poker is approximately 1/50. Use
the Poisson approximation to estimate the probability you will get at least one
three of a kind if yo...
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 Spring '10
 DURRETT
 The Land

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