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)
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?