Question

Let X and Y have the following joint probability density function f(x,y) = (3x, if I sysxs1 10, otherwise (a) Calculate Var (X+Y). (b) Find E(XY), E(Y|X), and E(E(X|Y)).

Answer 1

PAGE NO.:- DATE: / / EV): 1 2 (89-9") dy wancela (1473) - ( LI=) = 36-492 – 9. (1-8934 Nancy) - .41 30647-2 CON (X,Y)= E(XY) - E(X). Ely) E(XY) = 1 xy 3x dedy a ft x y de dy 220 $ [ gely? Tie stoep 3 (1 - 95)

ELHX) = s Gh-De ੫) EĽxista frang) da ਦੇ ਨੇ । + + ਲ =xJor - ਦੀ ਮਾਂ ( 5A

(੪ E (XY) : x. Paly) da (ah-1) & hp ਤੇ ਹੋ (੫॥5) : . f੧ ) ੧੩ g Xxx : : : E( E (੪॥੧)) : E Cx). ( ): . - 3 ਅਤੇ 2 3ਣ ਹੈ ਤੋਂ 0-1 ਹੈ 7

Joint density function. fy) = S 3x Us YSRST Lot o.w Calculate Var (fy) Var (x + y) = Var (x1 + Vanly) + 2 coulx,y) face) = * re dy = [say I* Ba? fly) = (34 de : [ )2-2.5 2311-99) 602 ['. Bet de - [ { xl]y 22.499 = (1-4) ECHI? S 2 (y - y²) dy = 23 y 4 7