08SimHw2

# 08SimHw2 - IEOR 4404 Assignment#2 Simulation Prof Mariana...

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

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: IEOR 4404 Assignment #2 Simulation September 17, 2008 Prof. Mariana Olvera-Cravioto Page 1 of 2 Assignment #2 due September 23rd, 2008 1. Suppose that X and Y are jointly discrete random variables with p ( x,y ) = x + y 30 , for x = 0 , 1 , 2 and y = 0 , 1 , 2 , 3 , otherwise. (a) Compute and plot p X ( x ) and p Y ( y ). (b) Are X and Y independent? (c) Compute and plot F X ( x ) and F Y ( y ). (d) Compute E [ X ], var( X ), E [ Y ], var( Y ), cov( X,Y ) and corr( X,Y ). 2. A particles velocity V is normally distributed with mean 0 and variance 2 . The particles energy is given by W = m V 2 2 , where m &amp;gt; 0 is a constant. (a) What is E [ W ] in terms of m and ? (b) What is the PDF of W ? 3. If X and Y have a joint probability density function specified by f ( x,y ) = 2 e- ( x +2 y ) , &amp;lt; x &amp;lt; , &amp;lt; y &amp;lt; find P ( X &amp;lt; Y ). 4. For any random variables X 1 , X 2 and any numbers c 1 , c 2 , show that var( c 1 X 1 + c 2 X 2 ) = c 2 1 var( X 1 ) + 2 c 1 c 2 cov(...
View Full Document

## This note was uploaded on 11/17/2010 for the course IEOR 4404 taught by Professor C during the Spring '10 term at Columbia.

### Page1 / 2

08SimHw2 - IEOR 4404 Assignment#2 Simulation Prof Mariana...

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

View Full Document
Ask a homework question - tutors are online