
Expectation
Hi I have a question regarding expectation of random variables.
An urn contains n+m balls, of which n are red and m are black. They are withdrawn from the urn, one at a time and without replacement. Let X be the number of red balls removed before the first black ball is chosen. We are interested in determining E[X]. To obtain this quantity, number the red balls from 1 to n. Now define the random variables Xi, i = 1,...,n, by
Xi = 1 if red ball i is taken before any black ball is chosen
Xi = 0 otherwise
a. Express X in terms of the Xi
b. Find E[X]
I got part a. I need help with part b. Thanks! =]