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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Asked Feb 20, 2020
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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

Note:

Hey, since there are multiple subparts are posted, we will answer first three subparts for you. If you want any specific subpart to be answered, then please submit that subpart only or specify the subpart number in your message.

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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