1. A product is classified according to the number of defects it contains and the factory that produces it. Let

X1 and X2 be the random variables that represent the number of defects per unit (taking on possible values

of 1, 2, or 3) and the factory number (taking on possible values 1, 2 or 3), respectively. The entries in the

table represent the joint possibility mass function of a randomly chosen product.

a. Please try to fill the missing part in table as below. Please explain what it means as P(X2=3 | X1=1 )=0?

b. Find the marginal probability distributions of X1 and X2.

c. Find E [X1 ], E[X2], Var(X1), Var(X2), and Cov(X1, X2).