Question

4. Suppose X and Y have the joint pdf f(x,y) = 6x, 0 < x < y < 1, and zero otherwise. (a) Find fx(x). (b) Find fy(y). (c) Find Corr(X,Y). (d) Find fy x(y|x). (e) Find E(Y|X). (f) Find Var(Y). (g) Find Var(E(Y|X)). (h) Find E (Var(Y|X)]. (i) Find the pdf of Y - X.

Answer 1

Given that:

  f(x,y) = 6x,0 < x < y < 1 and zero otherwise

find (a) fx(x)

(b) Find fy (y)

(c) Find Cor(X, Y)

(d) Find f(y|x)

(e) Find E(Y|X)

(f) Find Var(Y)

(g) Find V ar(E(Y|X)

) (h) Find E(Var(Y|X)) and (i) Find a pdf of Y
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(E! 1) dox-X as un-r) & Z Then & ta (v) = f 6 (v-ul du