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Unformatted text preview:  Z ∞∞ f XY ( zby a , y ) dy. Hint: Let W = Y be an auxiliary variable. 1 7. Let X and Y be independent with f X ( x ) = αeαx u ( x ) f Y ( y ) = βeβy u ( y ) . Determine the density of: (a) Z = X/Y . (b) Z = max( X, Y ) . 8. Show that if X, Y are i.i.d. N (0 , σ 2 ), then Z = X/Y has a Cauchy distribution, f Z ( z ) = 1 /π z 2 + 1 . Problems from Grimmet & Stirzaker. 1. Exercise 4.4.3. 2. Exercise 4.7.3. 3. Exercise 4.7.4. 4. Exercise 4.8.1 (Hint: Laplace transform) 5. Exercise 4.8.2 (Hint: Laplace transform) 2...
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 Spring '08
 Stites,M
 Probability, Probability theory, Monotonic function, Utah State University, ln X1 cos, ln X1 sin

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