Let W1, W2 be independent, each with a Cauchy distribution. In this exercise we find the pdf
Question:
(a) Show that the pdf of X1 = (1/2)W1 is
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(b) Let Y1 = X1 + X2 = W and Y2 = X1, where X2 = (1/2)W2. Show that the joint pdf of Y1 and Y2 is
-2.png)
(c) Show that the pdf of Y1 = W is given by the convolution formula,
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(d) Show that
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That is, the pdf of W is the same as that of an individual W.
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Step by Step Answer:
a w 1 2x 1 and dw 1 dx 1 2 Thus b For x 2 y 1 y 2 x 1 y 2 J 1 Thus g y 1 y 2 f y 2 fy ...View the full answer
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Related Book For 
Probability and Statistical Inference
ISBN: 978-0321923271
9th edition
Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman
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