(a) Find the value of A such that the following function is a joint density of two random variables: f(x, y) = Ae-x²-2y² (b) Let X, Y be the random variables admitting f from (a) as their joint density. Are X, Y independent? What is the distribution of each X, Y? (c) Let U, V be two random variables with joint density: fu,v(u, v) = Be Find B. (You may use the calculator for the rest of the problem.) (d) Find the marginal densities fu, fv. (e) Find the conditional fuv (ulv). Are U, V independent? -3u²+2uv-3v²

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