The joint pmf of X and Y is defined by f(x,y)=, x=1,2; y=1,2
(a) Find Cov(X,Y).
(b)Find E(X|Y=1)
a)
E(*X) = x*P(x,y) =(x2+2xy)/18
=(1^2+2*1*1)/18+(1^2+2*1*2)/18+(2^2+2*2*1)/18+(2^2+2*2*2)/18 =14/9
E(Y) = y*P(x,y) =(yx+2y2)/18
=(1*1+2*1^2)/18+(1*2+2*2^2)/18+(2*1+2*1^1)/18+(2*2+2*2^2)/18 =29/18
E(XY) = xy*P(x,y) =(x2y+2xy2)/18 =2.5
Covar(y,x)=E(XY)-E(X)*E(Y)= | 2.5-(14/9)*(29/18) =-1/162 |
b)P(Y=1) =P(X=1,Y=1)+P(X=2,Y=1) =(1+2*1)/18+(2+2*1)/18 =7/18
E(X|Y=1) =xP(x|y=1)
=(18/7)*(1*3/18+2*4/18)=11/7
The joint pmf of X and Y is defined by f(x,y)=, x=1,2; y=1,2 (a) Find Cov(X,Y)....
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