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**What is the mean of the sum of X and Y?**

(A) 1.2

(B) 3.5

(C) 4.5

(D) 4.7

(E) None of the above.

E(X) = 0 * (0.1 + 0.1) + 1 * (0.2 + 0.2) + 2 * (0.2 + 0.2) = 0 + 0.4 + 0.8 = 1.2

Next, we find the mean of Y.

E(Y) = Σ [ yi * P(yi) ]

E(Y) = 3 * (0.1 + 0.2 + 0.2) + 4 * (0.1 + 0.2 + 0.2) = (3 * 0.5) + (4 * 0.5) = 1.5 + 2 = 3.5

And finally, the mean of the sum of X and Y is equal to the sum of the means. Therefore,

E(X + Y) = E(X) + E(Y) = 1.2 + 3.5 = 4.7

Note: A similar approach is used to find differences between means. The difference between X and Y is E(X – Y) = E(X) – E(Y) = 1.2 – 3.5 = -2.3; and the difference between Y and X is E(Y – X) = E(Y) – E(X) = 3.5 – 1.2 = 2.3

Problem 2

The table on the left shows the joint probability distribution between two random variables – X and Y; and the table on the right shows the joint probability distribution between two random variables – A and B.

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