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Let f(x, y) = ( kxy + 1 2 if x, y ∈ [0, 1] 0...

Let f(x, y) = ( kxy + 1 2 if x, y ∈ [0, 1] 0 else denote the joint density of X and Y

a) Find k

b) Find the marginal density of X (because of the symmetry of the joint pdf, the marginal density of Y is analogous).

c) Determine whether X and Y are independent.

d) Find the mean of X

e) Find the cumulative distribution function of X. Set up an equation (but no need to solve) to find the median value of X.

f)Find the standard deviation of X

g) Set up (but you do not need to solve) an equation to find E (X/Y)

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