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J 1 A bag contains 2 fair dice with random variables X and Y. (a) Give the joint probability distribution of X and Y, and

J 1

A bag contains 2 fair dice with random variables X and Y. (a) Give the joint probability distribution of X and Y, and find the exact entropy E(X, Y) of this distribution, also check that E(X, Y)=E(X)+E(Y). (b) Show the sum of both results with W. Then calculate E(W) and show that E(W) < E(X, Y).

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