Math425hw5 - SPRING 2009 MATH 425 Ralf Spatzier Homework 5...

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

View Full Document Right Arrow Icon
SPRING 2009 MATH 425 Ralf Spatzier Homework 5 for Wednesday, June 10 (1) The random variables X and Y have the joint density function f ( x,y ) = 12 x y (1 - x ) for ) < x < 1 , 0 < y < 1 and equal to 0 otherwise. (a) Are X and Y independent? (b) Find E [ X ]. (c) Find E [ Y ]. (d) Find V ar ( X ). (e) Find V ar ( X ). (2) Three points X 1 ,X 2 ,X 3 are selected a t random on a line L of length 1. What is the probability that X 2 lies between X 1 and X 3 ? (3) Let X and Y have joint density function f ( x,y ) = 1 x 2 y 2 x 1 ,y 1 . (a) Compute the joint density function of U = XY and V = X/Y . (b) What are the marginal densities of U and V ? (4) The gross daily sales at Amer’s is a normal random variable with mean $2 , 200 and standard deviation $230. What is the probability that (a) that the total gross sales over the next 2 days exceed $5,000? (b) That the daily sales exceed $2,000 in at least 2 of the next 3 days? (5) Suppose
Background image of page 1

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

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 2

Math425hw5 - SPRING 2009 MATH 425 Ralf Spatzier Homework 5...

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

View Full Document Right Arrow Icon
Ask a homework question - tutors are online