math 411 homework8

# math 411 homework8 - Y have joint density f ( x,y ) = c ( x...

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

Department of Mathematics Fall 2011 Volodymyr Nekrashevych Math 411 — Problem Set 8 Issued: 11.01 Due: 11.09 8.1. Suppose X has density function f ( x ) for a x b and Y = cX + d , where c > 0. Find the density function of Y . 8.2. Suppose X is uniform on (0 , 1). Find the density function of Y = X n . 8.3. Suppose X has density function f ( x ) for - 1 x 1 and 0 otherwise. Find the density function of Y = | X | . 8.4. Suppose that X and
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Y have joint density f ( x,y ) = c ( x + y ) for 0 < x,y < 1. (a) What is c ? (b) What is P ( X < 1 / 2)? 8.5. Suppose X and Y have joint density f ( x,y ) = 1 for 0 < x,y < 1. Find P ( XY ≤ z ). 8.6. Suppose X is uniform on (0 , 1) and Y = X . Find the joint distribution function of X and Y . Does there exists joint density of X and Y ?...
View Full Document

## This note was uploaded on 02/13/2012 for the course MATH 411 taught by Professor Staff during the Fall '08 term at Texas A&M.

Ask a homework question - tutors are online