The joint density of Y1, Y2 is given by f(y) = k, −1 ≤ y1 ≤...

The joint density of Y1, Y2 is given by f(y) = k, −1 ≤ y1 ≤ 1, 0 ≤ y2 ≤ 1, y1 + y2 ≤ 1, y1 − y2 ≥ −1, 0, otherwise

a. Find the value of k that makes this a probability density function.

b. Find the probabilities P(Y2 ≤ 1/2) and P(Y1 ≥ −1/2, Y2 ≤ 1/2

c. Find the marginal distributions of Y1 and of Y2.

d. Determine if Y1 and Y2 are independent

e. Calculate E(Y1Y2).

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