Assignment_4 - option which allows me (if I wish to do so)...

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1 Assignment 4, STAT220-Winter 2011 Instructor: Kamyar Moshksar Due on March 11th, 2011 Problem 1 - A manufacturer of car radios ships them to retailers in cartons of n radios. The profit per radio is is $59.5, less shipping cost of $25 per carton, so the profit is $(59.5 n -25) per carton. To promote sales by assuring high quality, the manufacturer promises to pay the retailer $200 X 2 if X radios in the carton are defective (The retailer is responsible to repair those defective radios.). Suppose radios are produced independently and that %5 of radios are defective. How many radios should be packed per carton to maximize expected net profile per carton? Problem 2- Let X Bi( n,p ) . Calculate E (( X - 1) 3 ) . Hint. Use the moment generating function. Problem 3- Assume that each week a stock increases in value by $1 with probability 1 2 or decreases by $1 independently from week to week. The current price of the stock is $50. I wish to purchase a call
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Unformatted text preview: option which allows me (if I wish to do so) the option of buying the stock 13 weeks from now at a price of $55. Of course if the stock price at the time is $50 or less there is no benet of the option and it is not exercised. Assume that the return from the option is R = max( P-55 , 0) where P is the price of the stock in 13 weeks. Calculate E ( R ) . Problem 4-Let X be a r.v. with moment generating function M X ( t ) = 1 3 e-t-2 , t < ln 3 2 . Find f X ( . ) on R X . Problem 5-The number of calls an ofcer receives during a working day is a Poisson(5) random variable. The ofcer misses a call with probability . 01 independently from call to call. Find the probability that the ofcer answers exactly 10 calls in a working day....
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