The joint probability density function of two random variables X and Y can be represented as

(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 1 hour period, if the rst 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? (j) Compute the covarance and correlation coefficient of X1 and X2. (it) Determine the probability that the numbers of sub-standard rivets produced do not differ by more than 1 between one machine and the other. (I) 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