11/26/2012

Discussion of Group Projects

Sums of random variables

• Mean and variance for two random variables
• Mean and variance for more than two random variables
• Applications

Moment generating functions - any questions

• See tables on pages 358 and 359.

Bivariate normal distribution

• Find the marginal density of X.
• Theorem - If two random variables have a bivariate normal distribution, they are independent if and only if rho = 0.
• Class Exercise - If X and Y have a bivariate normal distribution, then the conditional distribution of Y given X=x is normal. Find the mean and variance of this conditional distribution.

We will have a problem session for Chapter 7 on Friday.