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Recitation4Solutions

# Recitation4Solutions - Steven Weber Dept of ECE Drexel...

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Steven Weber Dept. of ECE Drexel University ENGR 361: Statistical Analysis of Engineering Systems (Spring, 2008) Recitation 4 Solutions (Friday, April 25) Question 1. A computer store purchases n computers from the manufacturer at a price of p dollars per computer. The store sells the computers at a price of q > p dollars per computer. The manufacturer agrees to buy back the unsold computers at a price of r < p dollars per computer. The number of sold computers is a uniform random variable, meaning the probability of selling k computers is 1 / ( n + 1) for each k = 0 , 1 , 2 , . . . , n . Please do the following: 1. Let X be a rv denoting the number of sold computers. Write down a function for the profit (revenue minus costs) in terms of X, p, q, r, n . h ( X ) = qX + ( n - X ) r - np = ( q - r ) X - ( p - r ) n. (1) 2. Compute the expected value of the profit. Hint: the sum of the first n integers is n ( n + 1) / 2 . E [ h ( X )] = E [( q - r ) X - ( p - r ) n ] = ( q - r ) E [ X ] - ( p - r ) n = ( q - r ) n k =0 kp ( k ) - ( p - r ) n = ( q - r ) 1 n + 1 n k =0 k - ( p - r ) n = ( q - r ) n 2 - ( p - r ) n = n q + r 2 - p . (2) www.ece.drexel.edu/faculty/sweber 1 April 25, 2008

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Steven Weber Dept. of ECE Drexel University Question 2. Let X have pmf: p ( k ) = P ( X = k ) = (1 - p ) p k 1 - p n +1 , k = 0 , . . . , n (3) for some positive integer n and some p
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Recitation4Solutions - Steven Weber Dept of ECE Drexel...

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