# A box contains three cards, labeled 1, 2, and 3. Two cards are chosen at random, with the first card being replaced before the second card is drawn. Let X represent the number on the first card, and let Y represent the number on the second card. Assume the first card is not replaced before the second card is drawn. a) Find the joint probability mass function of X and Y. b) Find the marginal probability mass functions pX(x) and pY(y). c) Find µX and µY. d) Find µXY. e) Find Cov(X,Y).

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A box contains three cards, labeled 1, 2, and 3. Two cards are chosen at random, with the first card being replaced before the second card is drawn. Let X represent the number on the first card, and let Y represent the number on the second card. Assume the first card is not replaced before the second card is drawn. a) Find the joint probability mass function of X and Y. b) Find the marginal probability mass functions pX(x) and pY(y). c) Find µX and µY. d) Find µXY. e) Find Cov(X,Y).

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Step 1

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For calculating probability mass functions, we are considering first card being replaced before the second draw. We have tried our best to solve this problem.

Step 2

a)

A box contains three cards labeled 1, 2, and 3.Two cards are drawn at random, with the first card being replaced before the second draw. Let X denotes that the number on the first card and Y be the number on the second card.

The joint probability mass function of X and Y ...

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