160a09_hw7

# 160a09_hw7 - 1 Suppose it starts with full reserves at the...

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Winter 2009 Pstat160a Homework #7 Due Wednesday, March 11 All problems are from Chapter 4. Problem 1. Pb 24, p. 267 Problem 2. Pb 30, p.268 Problem 3. Pb. 46, p 271 Problem 5. (Actuarial type of problem) A water distribution company in southern California gets its water supply from the north and sell it back to its customers in Orange county. Assume the following simpliﬁed scheme: 3 MG (millions of gallons) of water arrives from the north at the beginning of the month. The company can store up to 4 MG. If it has any excess beyond that, it sells it immediately to another distributor for agricultural usage. The monthly usage in Orange county varies randomly: it is 1 MG with probability .1 2 MG .2 3 MG .6 4 MG .1 If at any time, it is not able to meet the demand, it loses its licence.
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Unformatted text preview: 1) Suppose it starts with full reserves at the beginning of the ﬁrst month (after restocking). What is the expected amount of water it can sell as surplus after 3 months? 2) Under that scheme, what is the probability that the company loses its licence at some point in the future? What is the probability it does so in the ﬁrst 5 months? 3) Suppose that when the company is not able to meet demands, it can buy water from another supplier and so it is always able to meet demands. What is the probability it had to buy some water from the other supplier in the ﬁrst 5 months? In the long-run, what is the average MG/month it buys, and what average number does it sells to this other supplier?...
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