In: Statistics and Probability
Let X and Y be independently and identically distributed random variables. Then, what is P (X < Y )
(a) in case the common distribution of X and Y is continuous?
(b) in case P(X=i)=P(Y =i)= 1, i=1,2,···,n.
Note: I think theres a typo in part b) as it will be P(X=i)= P(Y=i) = 1/n , for i=1,2,3,...,n . Because the pmf must sum to 1.
So proceeding with that the solution to both the parts is given in the image below. Check them out>>>