Let Joint pmf of X and Y be defined as f(x,y) = (x + y)/32 x=1,2, y=1,2,3,4
Find (i)P(X > Y) (ii)P(Y=2X) Thanks
$\displaystyle P(X>Y)=P(X>Y,Y=1)+P(X>Y,Y=2)$ $\displaystyle +P(X>Y,Y=3)+P(X>Y,Y=4)$
but since X=1 or 2, it is not possible that X>Y if Y=2,3 or 4.
So this probability is actually :
$\displaystyle P(X>Y)=P(X>Y,Y=1)=P(X>1,Y=1)$
The only possible value for X, such that X>1 is X=2.
So $\displaystyle P(X>Y)=P(X=2,Y=1)=f(2,1)$
$\displaystyle P(Y=2X)=P(Y=2X,X=1)+P(Y=2X,X=2)=P(Y=2,X=1)$ $\displaystyle +P(Y=4,X=2)=f(1,2)+f(2,4)$(ii)P(Y=2X) Thanks