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Math Help - joint pmf

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    joint 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
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    Quote Originally Posted by jojo_jojo View Post
    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)
    P(X>Y)=P(X>Y,Y=1)+P(X>Y,Y=2) +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 :
    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 P(X>Y)=P(X=2,Y=1)=f(2,1)

    (ii)P(Y=2X) Thanks
    P(Y=2X)=P(Y=2X,X=1)+P(Y=2X,X=2)=P(Y=2,X=1) +P(Y=4,X=2)=f(1,2)+f(2,4)
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