Thread: Expected value problem

Hey i'm having a little trouble with expected value so i don't really understand how to do this problem:

Assume that N people check their hats and the hats are handed back to them at random. Let X_j = 1 if the jth person gets his or her hat and 0 otherwise. Find E(X_j) and E(X_j * X_k) for j not equal to k. Are X_j and X_k independent?

Thanks!

since (1)(1)1 =1 and (0)(0)=0=(0)(1)

X_j=1 if this person gets his/her hat 0 otherwise
so E(X_j)=p(J th person get their hat)

and X_j * X_k= 1 iff both get their hats

so E(X_j * X_k)=P(both the j th and k th people get their hats)

thank you!
so is p(X_j) = j*(j-1)! ?
but I'm not sure how to find p(X_k) or p(X_j * X_k)...

probabilities do not exceed 1