Let X and Y have a continuous distribution with joint probability density function f(x,y) = { x + y for 0 ? x ? 1 and 0 ? y ? 1, 0 otherwise. Compute the covariance Cov(X,Y).
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Step 1
First, we need to find the expected values of X and Y: E(X) = ∫∫ x f(x,y) dxdy = ∫∫ x dydx = ∫0^1 ∫0^1 x dx dy = 1/2 E(Y) = ∫∫ y f(x,y) dxdy = ∫∫ y dydx = ∫0^1 ∫0^1 y dx dy = 1/2 Show more…
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