Find es t and var s t 239 messages arrive to be

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Unformatted text preview: ute 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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