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Q: Assistance in understanding and solving this example from Probability and Statistical (Conditional Distributions) with the steps of the solution to better understand, thanks.

**Please give the step by steps with details to completely see how the solution came about.

1) Suppose X and Y both take values in [0,1] with joint probability density f(x,y) = 4xy.

a) Find fx(x) and fy(y), the marginal probability density functions.

b) Are the two random variables independent? Why or why not?

c) Compute the means and variances of X and Y.

d) Find P(X \leq Y).

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