Question

Let X and Y be two random variables with joint probability mass function:

(?,?) = (??(3+?))/(18*3+30)??? ?=1,2,3 ??? ?=1,2

(?,?) = 0, Otherwise.

• Find P(X>Y)

and

Let X and Y be two random variables with joint probability mass function:

(?,?) = (??(4+?))/(18*4+30)??? ?=1,2,3 ??? ?=1,2

(?,?) = 0, Otherwise.

• Find P(Y=2/X=1)

1)P(X>Y)=P(X=2,Y=1)+P(X=3,Y=1)+P(X=3,Y=2)=2*1*(3+1)/84+3*1*(3+1)/84+3*2*(3+2)/84=0.595

2)P(Y=2|X=1)=P(X=1,Y=2)/P(X=1)=0.117647/0.1666667=0.706

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