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 p 1 (x) for X c Find the marginal probability distribution p 2 (y) for Y d Find the conditional probability distribution p 1 (x y) e Find the conditional probability distribution p 2 (y x) 1 4 5 050 025 0 025 Y 1 200 050 300 100 100 150 2

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Question: 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 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.

1 4 5 .050 .025 0 .025 Y 1 .200 .050 .300

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).

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

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