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E (t L) (b) What happens when we let t ! 1 in the answer to (a)?
2.30. Customers arrive according to a Poisson process of rate per hour. Joe
does not want to stay until the store closes at T = 10PM, so he decides to close
up when the ﬁrst customer after time T s arrives. He wants to leave early
but he does not want to lose any business so he is happy if he leaves before T
and no one arrives after. (a) What is the probability he achieves his goal? (b)
What is the optimal value of s and the corresponding success probability?
2.31. Customers arrive at a sporting goods store at rate 10 per hour. 60% of
the customers are men and 40% are women. Women spend an amount of time
shopping that is uniformly distributed on [0, 30] minutes, while men spend an
exponentially distributed amount of time with mean 30 minutes. Let M and
N be the number of men and women in the store. What is the distribution of
(M, N ) in equilibrium.
2.32. Let T be exponentially distributed with rate . (a) Use the deﬁnition of
conditional expec...
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 Spring '10
 DURRETT
 The Land

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