Let X and Y be two jointly continuous random variables with joint PDF f_{XY}(x,y) = { 1/2x + 1/4y 0 <= x <= 1, 0 <= y <= 2 0 otherwise Find the marginal PDFs, f_X(x) and f_Y(y). Find P(X > Y).
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Step 1
For fx(x): fx(x) = ∫fxy(x, y) dy, where the integral is taken over the range of y (0 to 2) fx(x) = ∫(x + 2y) dy from 0 to 2 (since x is between 0 and 1, and y is between 0 and 2) Now, integrate with respect to y: fx(x) = [xy + y^2] from 0 to 2 fx(x) = (2x + 4) Show more…
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