Let fxy18 0y4 yxy2 be the joint pdf of X and Y a Sketch the

Let f(x,y)=1/8, 0y4 yxy+2 be the joint pdf of X and Y.

(a) Sketch the region for which f(x,y)>0

(b) Find fx(x), the marginal pdf of X.

(d) Determine h(y|x) the conditional pdf of y given X=x.

(e) Determine g(x|y) the conditional pdf of x given Y=y.

(f) Compute E{Y|x}

(g) Is the conditional mean of Y a linear function of x?

Please show me the solution plz.

Here y varies from 0 to 4, x from y to y+2

fx(x) = \\int_{0}^{4}\\frac{dy}{8}

= 0.5, 0<x<2

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c) fy(y) = \\int_{0}^{2}\\frac{dx}{8}

= 0.25, 0<=y<=4

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f(x) f(y) = 0.5(0.25)

= 1/8

Hence x and y are independent.

d) h(y/z) = h(y) = 0.25, 0<y<2

e) G(x/y) = fx(x) as x and y are independent.

f) E(Y./x) = E(Y) = 2

g) No not a linear funciton