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Unformatted text preview: Mathematical Statistics-992 Homework #6 Due 5/12/2011 1. From textbook: Chapter 6 12, 21, 24, 37, 42 Chapter 7 1, 4, 7, 17, 29, 33, 34, 38, 45, 46 2. Let X and Y be independent continuous random variables with marginal density functions f x and f x . (1) Show that U X Y has pdf fU u f vf u v dv. (Do this by DF method and transformation method). (2) Let X and Y be independent continuous random variables with marginal density functions N µ , σ and N µ , σ . Use (1) to show that U follows N µ µ ,σ σ. 3. Let X , X , density f x, θ ,X X Y be independent random variables each having an exponential e ,x 0. Define Y , Y , , Y by Y X X X, 1 i n. (1) Find the inverse of this transformation. What is the value of the Jacobian. (2) Find the density of Y , Y , ,Y . 4. Let X ~ N µ, σ . Find the pdf of S eX (S is said to follow the log normal distribution), E S , and V S . (Hint: use the mgf of normal distribution). ...
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This note was uploaded on 05/09/2011 for the course DIF 1486 taught by Professor Yow-jenjou during the Spring '11 term at National Chiao Tung University.
- Spring '11