A standard deck of 52 cards is shuffled and dealt. Let $X_1$ be the number of cards appearing before the first ace, $X_2$ the number of cards between the first and second ace (not counting either ace), $X_3$ the number between the second and third ace, $X_4$ the number between the third and the fourth ace, $X_5$ the number after the last ace. It can be shown that each of these random variables $X_i$ has the same distribution, $i=1,2,...,5$, and you can assume this to be true.
a) Write down a formula for $P(X_i=k),0\le k \le 48$.
b) Show that $E(X_i) = 9.6$ [Hint: Do not use your answer to a).]
c) Are $X_1,...,X_5$ pairwise independent? Prove your answer.
I could get some numerical answers for specific $X_i$, but don't know how to get a formula for the general case.