Two machines produce a certain item. The capacity per day of machine 1 is 1 unit and

Question:

Two machines produce a certain item. The capacity per day of machine 1 is 1 unit and that of machine 2 is 2 units. Let (X1, X2) be the discrete random variable that measures the actual production on each machine per day. Each entry in the table below represents the joint probability, for example, PX1X2 (0,0) = 1/8.

(a) Find the marginal distributions of X1 and X2.
(b) Find the conditional distribution of X1, given X2 = 1.
(c) Are X1 and X2 independent random variables?
(d) Find E(X1), E(X2), variance (X1), and variance (X2).
(e) Find the probability distribution of (X1 + X2).

Distribution
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