Question

for 1 Sx soo and 2. Suppose that X and Y are continuous and jointly distributed by the function f(x,y) = 1 Sy S. PAY ATTENTION TO THE SUPPORT REGION. a. Find the marginals for X and Y. b. Find the conditional probability density functions g(xly) and hylx). C. Determine whether or not X and Y are independent based on your results above. d. Calculate P(X+Y<5 Y = 3). e. Find E[X] f. Find E[Y] 8. Find E[XY] h. Find cov(X,Y) i. Find the correlation coefficient.

Answer 1

solution & Griven and jointly distributed - x by and the y are continuous function saso and sycoo © Find the marginals of X and Y :- marginal of x is fos= ro y dy | ffc) = 2 h 1sxsoo marginal of Y is +14) = do ox +13= sysco/ conditional Probability density Find the function- - Hany) ty) 41043 1944x)= 15x5

| (i) Al Hz) = (남) 로 | F ) Al ) - 0 15 50 / H4Y = fJ 삐 x and y are independent. | @ calculate P[x+Y45) Y=3] ⇒ PLx <3 / Y-3] - PLx<2] - J . | 2 - 읍 씰 ⓐ Ek)= j | . 2x2x | 5 2 | E(V) = g dy 52g - 2 -

@ ELXY) = SOL my. By tady - $ Lº + x2y+ trady 7+ (), = + Ang CoveX,Y) = E(XY) – EK) EV) z 4-4 zo Ang © io correlations come = 0 Ang