Do Problem 2 ONLY please.
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 They are withdrawn from the urn, one at a time and without replacement.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. Find 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
a) Express X in terms of the Xi
b) Find E[X]
From the above problem, let Y = number of red balls chosen after the first but the second black ball has been chosen
a) express Y as the sum of n random variables, each of which is equal to either 0 or 1
b) find E[y]
a) Let Yi be a randon variable which is 1 if the ith ball drawn after the first black ball ...