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Let Ω = {0, 1}^3 , that is, all possible (ordered) triples of zeros and ones....

Let Ω = {0, 1}^3 , that is, all possible (ordered) triples of zeros and ones.

Suppose that all outcomes have equal probability.

We define three random variables X1, X2, and X3 on this space representing the first, second, and third digit, respectively.

We also define X = X1 + X2 + X3.

(i) Compute the values (across Ω) of each of the following random variables: E(X|X1), E(E(X|X1)|X2), E(X2|X).

(ii) What is the probability mass function of E(X2|X).

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