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

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- Mar 18th 2009, 10:27 AMjojo_jojojoint pmf
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 - Mar 18th 2009, 10:41 AMMoo
$\displaystyle P(X>Y)=P(X>Y,Y=1)+P(X>Y,Y=2)$ $\displaystyle +P(X>Y,Y=3)+P(X>Y,Y=4)$

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 $\displaystyle P(X>Y)=P(X=2,Y=1)=f(2,1)$

Quote:

(ii)P(Y=2X) Thanks