Question

Student ID: Let the discrete RV X-UI-2,2]. Let Y X2 a) 14pts] What values X and Y can take? Find pdf's of both X and Y. b) [4pts] Compute the joint pdf, xy(x) c) [4pts] Compute the Ech) and Em d) [3pts] Compute the Cov(x.y e) [3pts] Compute the pxy Cor(x,Y). f) 2pts] Are X and Y independent? Prove it.

Answer 1

Ne have (a x can take values ince y: "The Pdf 여 x ; 5 5 5 o-therwise 0 P(xex) 2. 느n

(b y The 卜dt joint f,y(X,y 4 了一 5 5 Sina, y can take valua 4- iff x=-2 or 2 X- 5 E(x)O : E(x) 0

5 2 E (Y) 2 (d) Cov (xx) for Cov (XY)-E (XY)-E (x) E (y) 、、 x 1 5 E (Xy)

Var(x) Var(y) Cov (x,y) since : and Y au not ndppendant o-t and Y But hess Hence X and Yaot independent