Question

. A certain supermarket has both an express checkout line and a super-express checkout line. Let X1 denote the number of customers in line at the express checkout at a particular time of day, and let X2 denote the number of customers in line at the super-express checkout at the same time. Suppose the joint probability distribution of X1 and X2 is as follows

x2

0 1 2

0 0.1 0. 1 0.0

x1 1 0.1 0.2 0.1

2 0.0 0.1 0.3

(a) Find P(X1 = X2). (4 pts.)

(b) Find P(X1 6= 0). (4 pts.)

(c) Find the marginal distribution of X1. (4 pts.)

(d) Find Cov(X1, X2). (4 pts.)

(e) Are X1 and X2 independent? Why? (4 pts.)

Answer 1