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Unformatted text preview: 36-225 Handout for Lecture # 11
September 19, 2008
1. Consider the following two random variables: Y - the daily number of defective products coming out of production line A. X - the daily number of defective products coming out of production line B. Y and X have the following probability distributions: y, x P (Y = y) P (X = x) Find E(Y ) and E(X). 0 .15 .05 1 .3 .05 2 .25 .1 3 .2 .75 4 .1 .05 2. Suppose you work for an insurance company, and you sell a $150,000 whole-life insurance policy at an annual premium of $1250. Actuarial tables show that the probability of death during the next year for a person of your customer's age, sex, health, etc., is 0.005. (a) What is the expected gain (amount of money made by the company) for a policy of this type? (b) Suppose that five years have passed and your actuarial tables indicate that the probability of death during the next year for a person of your customer's current age is .008. Obviously, this change in probability should be reflected in the annual premium. What should be the annual premium (instead of $1250) if the company wants to keep the same expected gain? 3. Consider the random variable Y from example 1. Assume that if there are y defective products, the cost is g(y) = 5 y 2 . Find the expected cost. 4. A store owner has overstocked a certain item and decides to use the following promotion to decrease the supply. The item has a marked price of $100. For each customer purchasing the item in a particular day, the owner will reduce the price by a factor of one-half. Thus the first customer will pay $50, the second customer will pay $25 and so on. Suppose that the number of customers who purchase the item during a day (Y ) the following p.d.f: PY (y) = e-2 2y y! y = 0, 1, 2, 3 . . . Find the expected cost of the item at the end of the day. 5. Back to the r.v. Y in example 1 above. Assume now that the daily cost for maintaining production line A is $150, and that the cost due to y defective products is 5y + y 2 . Find the expected daily cost of operating the production line. ...
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- Spring '11
- Statistics, Probability theory, probability density function, insurance company, defective products