Let X and Y have the joint pdf f(x,y) = 6(1-x-y), x+y<1, 0 < x, 0 < y, zero elsewhere. Compute the marginal distributions as well as P(2X+3Y < 1) and E(XY + 2X^2).
Added by Jose K.
Step 1
First, we need to find the marginal distributions of X and Y. To find the marginal distribution of X, we need to integrate the joint pdf with respect to Y: f_X(x) = ∫f(x,y) dy = ∫6(1-x-y) dy, where the limits of integration are from 0 to (1-x). f_X(x) = Show more…
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