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Suppose a scientist is measuring a jointly distributed pair of quantities X and Y and finds...

Suppose a scientist is measuring a jointly distributed pair of quantities X and Y and finds that they obey the following distribution

P(X, Y ): P(−1, −1) = 1/15, P(0, −1) = 1/10, P(1, −1) = 1/6 P(−1, 0) = 1/30, P(0, 0) = 2/15, P(1, 0) = 1/6 P(−1, 1) = 7/30, P(0, 1) = 1/10, P(1, 1) = 0

(a) Find P(X=k) for k = −1, 0, 1, and find E(X).

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