problemset26

problemset26 - Y . 4 5. Suppose X,Y has joint density f X,Y...

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
STAT/MA 416 October 28, 2011 Problem Set 26 Name: 1. Consider a pair of random variables X,Y with constant joint density on the triangle with vertices at (0 , 0), (3 , 0), and (0 , 3). a. Find the expected value of the sum of X and Y , i.e., find E ( X + Y ). b. Find the variance of X , i.e., find Var( X ). 1
Background image of page 1

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

View Full DocumentRight Arrow Icon
2. Consider a pair of random variables X,Y with constant joint density on the quadrilateral with vertices (0 , 0), (2 , 0), (2 , 6), (0 , 12). a. Find the variance of X , i.e., find Var X . b. Find the variance of Y , i.e., find Var Y . 2
Background image of page 2
3. Let X,Y have joint density f X,Y ( x,y ) = 14 e - 2 x - 7 y for x > 0 and y > 0; and f X,Y ( x,y ) = 0 otherwise. Find the variance of the sum of X and Y , i.e., find Var( X + Y ). 3
Background image of page 3

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

View Full DocumentRight Arrow Icon
4. Let X,Y have joint density f X,Y ( x,y ) = 18 e - 2 x - 7 y for 0 < y < x ; and f X,Y ( x,y ) = 0 otherwise. Find the variance of
Background image of page 4
Background image of page 5

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

View Full DocumentRight Arrow Icon
Background image of page 6
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Y . 4 5. Suppose X,Y has joint density f X,Y ( x,y ) = ( 1 9 (3-x )(2-y ) if 0 x 3 and 0 y 2, otherwise. Find the expected value of X 2 + Y 3 , i.e., nd E ( X 2 + Y 3 ). 5 6. Design your own problem and solution. Create your own problem about the expected value of a function of a continuous random variable, or about the variance of a continuous random variable. Design your problem in such a way that you would nd it enjoyable and also interesting (i.e., not completely trivial) if you found this problem in a probability book. Please provide the answer for your problem too. 6...
View Full Document

Page1 / 6

problemset26 - Y . 4 5. Suppose X,Y has joint density f X,Y...

This preview shows document pages 1 - 6. Sign up to view the full document.

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