# Question

A group of 20 people consisting of 10 men and 10 women is randomly arranged into 10 pairs of 2 each. Compute the expectation and variance of the number of pairs that consist of a man and a woman. Now suppose the 20 people consist of 10 married couples. Compute the mean and variance of the number of married couples that are paired together.

## Answer to relevant Questions

Let X1, X2, . . . ,Xn be independent random variables having an unknown continuous distribution function F, and let Y1,Y2, . . . ,Ym be independent random variables having an unknown continuous distribution function G. Now ...A fair die is successively rolled. Let X and Y denote, respectively, the number of rolls necessary to obtain a 6 and a 5. Find (a) E[X]; (b) E[X|Y = 1]; (c) E[X|Y = 5]. Consider the following dice game: A pair of dice is rolled. If the sum is 7, then the game ends and you win 0. If the sum is not 7, then you have the option of either stopping the game and receiving an amount equal to that ...An urn contains 30 balls, of which 10 are red and 8 are blue. From this urn, 12 balls are randomly withdrawn. Let X denote the number of red and Y the number of blue balls that are withdrawn. Find Cov(X, Y) (a) By defining ...Suppose that in Problem 70 we continue to flip the coin until a head appears. Let N denote the number of flips needed. Find (a) P{N ≥ i}, i ≥ 0; (b) P{N = i}; (c) E[N]. Problem 70 Consider an urn containing a large ...Post your question

0