Four women, A, B, C, and D, check their hats, and the hats are returned in a random manner. Let [math]\Omega[/math] be the set of all possible permutations of A, B, C, D. Let [math]X_j = 1[/math] if the [math]j[/math]th woman gets her own hat back and 0 otherwise. What is the distribution of [math]X_j[/math]? Are the [math]X_i[/math]'s mutually independent?