Two machines produce rivets for a factory job. The number of sub-standard rivets per hour by the two machines are random variables, denoted by X1 and X2

Two machines produce rivets for a factory job. The number of sub-standard rivets. per hour by the two machines are random variables, denoted by X; and X2. The bivariate PM? of X1 and X2, PX1X1 ( x1, 1|:2 ) , is given in the table below. X2=0 X2=1 X2=2 X2=3 X1 = 0 0 07 0.05 0 02 0 01 X1 = 1 0 05 016 0.12 0 02 X1=2 002 0.12 01? 005 X1 =3 0 01 0 01 0.05 0 0? (g) In a 1 hour period, if the rst machine produces exactly 2 sub-standard rivets, What is the probability that the second machine produces at least one sub-standard rivet. (h) In a I hour period, if the first machine produces at least 2 sub-standard rivets, what is the probability that the second machine produces at least one sub-standard rivet. (i) Are random variables X1 and X2 statistically independent? U) Compute the covarance and correlation coefficient of X1 and X2. (k) Determine the probability that the numbers of sub-standard rivets produced do not differ by more than 1 between one machine and the other. (1) The factory manager estimated that an older machine, which was replaced, produced Y = X1+X2 substandard rivets per hour. Derive the marginal PMF of the number of sub-standard rivets per hour Y produced by the older machine