Suppose that X and Y are continuous random variables with the following joint p.d.f.: (a) Find...

Question

Question

Suppose that X and Y are continuous random variables with the following joint p.d.f.:

fxy(x, y)- o otherwise

(a) Find fX|Y =y(x|y).

(b) Calculate EX[X|Y = y]

(c) Calculate VarX[X|Y = y]

(d) Calculate E[Y]

(e) Show that VarY [EX(X|Y = y)] = VarY [2/3Y ].

(f) Find VarX(X|Y = 1/2)

(g) Find EX[X|Y = 0.2]

(h) Without any calculation, what is P(X < Y )? Explain your answer.

(i) Without any calculation, what is FX,Y (2,2)? Explain your answer.

Answer 1

Answer #1

xy (x, z 2 D 32° 了 2 0 18 0 ams 18 3 fry (2,7) 1

Answer 2

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