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M362K Sample Test 3A - M362K Sample Test 3A Dr Gary Berg...

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M362K Sample Test 3A Dr. Gary Berg All problems are worth ten points. Do ten of the twelve problems. Clearly mark the problems to be omitted. Show your work. 1) The joint density function of X and Y is given by f ( x , y ) = 2 e x e 2 y for positive x and y and is zero otherwise. Find P ( X < Y ) . 2) Suppose that 3 balls are chosen without replacement from an urn consisting of 5 white and 8 red balls. Let X i equal 1 if the i th ball is white, and is 0 otherwise. Give the joint probability mass function of X 1 , X 2 . 3) If X and Y are independent continuous positive random variables, express the density function of Z = X / Y in terms of the density functions of X and Y . 4) A television store owner figures that 45 percent of the customers entering his store will purchase an ordinary television set, 15 percent will purchase a plasma television set, and 40 percent will just be browsing. If 5 customers enter the store on a given day, what is the probability that he will sell 2 ordinary sets and 1 plasma set on that day?
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