2. Let X and Y be continuous random variables having the joint density function: [c(x² + y²) 0 f(x, y) = 0≤x≤1, 0≤y≤1 otherwise Determine a) The constant c b) P(X< 1/2, Y> 1/2) c) P(1/4 < X < 3/4) d) P(Y<1/2) e) The conditional distribution of X given Y=y f) Whether or not X and Y are independent.

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