Question

Suppose X, Y are random variables whose joint PDF is given by fxy(x,y) = { 0<y<1,0<=<y 0, otherwise 1. Find the covariance of X and Y. 2. Compute Var(X) and Var(Y). 3. Calculate p(X,Y)

Answer 1

For the nandom vaniable, X, Y Zëren joint poor is for Cosy) = { 1 yo oozy <1, o<x<y *** o Otherwise you can norge conite this por as like this (34) ocacy<1 Otherwise WO oslan Sxy 2 VI

E Cx) = fe abydo= 67 Crete) ay dy = fully y 10 Comedi 2 = { [ = 1/2 x 1/2 = 2/6 1 y ELNI dy to [[ta) y dy = {{ [2] ydy = {*y-ythin هه بود و رنگی pagedy (12) - ģ

ECXV] S nyot y dyda be dy dx = Budge) dy es 2. dy - Iris 6 1 플들 중 1:) se covarienee CX,Y) OBSC - Elxy] - E[x] ELY) 등등 등 그 시 후 3 - -

x2) 2) Van (X) = E(X) - (E(x))? &C x 35 2 d. 1 day da 9 ? dre) ydy gdy 1 y = ( g 3 - [ m 1 6 1 alors lop T 1 / 1 y y sy dg = [ 2/2 27 / som var (X)= E(+2) – CEx)) ? 1 3 5 1 98 1 15 1 15 5 -(6) = 0.0389

g E(re) = fs 8 1 1 ♡ 1 dady = f ( 24 de ordy [x] G g zdy y. yhdy = 1 *ysy=[*** so, von (YD= EC427 – E[Y])2 4 4 2 1 - ( 2 / 1 / 4 - 2 / 4 0.139 82 p(x, y) = Covanience (x,y) van (X) x van(y 1 9 = 10.0989 x0.139 = 1.51