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# Let W1,W2 be independent, each with a Cauchy distribution. ISBN: 9780321923271 41

## Solution for problem 12E Chapter 5.2

Probability and Statistical Inference | 9th Edition

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Problem 12E

Let W1,W2 be independent, each with a Cauchy distribution. In this exercise we find the pdf of the sample mean, (W1 +W2)/2.

(a) Show that the pdf of X1 = (1/2)W1 is (b) Let Y1 = X1 + X2 = and Y2 = X1, where X2 = (1/2)W2. Show that the joint pdf of Y1 and Y2 is (c) Show that the pdf of Y1 = is given by the convolution formula, (d) Show that That is, the pdf of is the same as that of an individual W.

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##### ISBN: 9780321923271

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