Mathematical Statistics HW#6-992

# Mathematical Statistics HW#6-992 - Mathematical...

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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). ...
View Full Document

## 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.

Ask a homework question - tutors are online