A software program is designed to perform two tasks, A and B. Let X represent the number of IF-THEN statements in the code for task A and let Y represent the number of IF-THEN statements in the code for task B. The joint probability distribution p(x, y) for the two discrete random variables is given in the accompanying table.

a. Verify that the properties of a joint probability distribution hold.
b. Find the marginal probability distribution p₁(x) for X.
c. Find the marginal probability distribution p₂(y) for Y.
d. Find the conditional probability distribution p₁ (x Ι y).
e. Find the conditional probability distribution p₂ (y Ι x).

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1 4 5 .050 .025 0 .025 Y 1 .200 .050 .300 .100 .100 .150 2.