Question: Problem 1. Suppose Xi i = 1, 2, ..., n are independent Exp(1). (a). Let Y = 2X(X1+ X2+ . .. + Xn). Show that

Problem 1. Suppose Xi i = 1, 2, ..., n are independent Exp(1). (a). Let Y = 2X(X1+ X2+ . .. + Xn). Show that Y is a chi-square random variable. hint: compute the MGF of Y.] (b). Now suppose we observed n samples from Exp()). Use (a) to construct an EXACT 95% confidence interval of 1. [hint: follow the example on page 29 in handout 7.]

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