# hw9 - Guidance: Use the fact that χ 2 is a special case of...

This preview shows pages 1–2. Sign up to view the full content.

STAT 225 - Homework 9 Due Thursday 6/25 Do the following problems : 1. Let the random variable X have the following density function: f X ( x ) = αθ α x α +1 x > θ α > 0 , θ > 0 0 otherwise Find the distribution of Y = ln X θ 2. Let X exp( β ). Find the distribution of Y = e - X/β and identify the disttribution you got. 3. Page 318, problem 6.34 ( Hint: For (b) E ( Y ) = E ( U 1 2 ) = ... and E ( Y 2 ) = E ( U ) = ... 4. Let X N ( μ , σ 2 ). The random variable Y = e X is said to have a log - normal distribution with parameters μ and σ . (a) Find the density function of Y . (b) Find E ( Y ) and V ( Y ) ( Hint: do not integrate. Use the relationship between X and Y and the moment generation function of X ) 5. Page 324, problem 6.49 6. page 324, problem 6.57 7. page 325, problem 6.59

This preview has intentionally blurred sections. Sign up to view the full version.

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

Unformatted text preview: Guidance: Use the fact that χ 2 is a special case of Gamma, and the result you proved in the previous problem. 8. Page 323, problem 6.40 Guidance: Use a result from class about the distributions of Y 2 1 and Y 2 2 , and the result you proved in the previous problem. 1 9. Page 323, problem 6.41 10. Page 375, problem 7.49 11. Page 388, problem 7.96 12. Let X 1 ,X 2 ,...,X n be independent random variables, all having a Beta( α , 1) distri-bution. (a) Prove that X ( n ) also has a beta distribution and identify the parameters. (b) Based on part (a), what is E ( X ( n ) )? 2...
View Full Document

## This note was uploaded on 07/15/2011 for the course STAT 36225 taught by Professor Tom during the Summer '09 term at Carnegie Mellon.

### Page1 / 2

hw9 - Guidance: Use the fact that χ 2 is a special case of...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online