10 tennis players participate in a round robin tournament. This means thatevery player plays everybody else exactly once, hence each player plays 9 matches. Assumethat the outcomes of the matches are random: in each match each of the two players winswith probability 0.5 independently of the outcomes of the other matches. (a) Compute the expected number of players that have exactly 2 wins.(
(b) LetXbe the random variable of the number of players that have exactly 0 wins. ComputeE(X).
(c) ComputeE(X(X−1)).
(d) ComputeV ar(X).
(e) Compute thenth factorial momentE(X(X−1)...(X−n+ 1)).
(f) Compute thenth momentE(Xn) for alln≥1.
(g) (Bonus) Compute the moment generating functionMX(t) ofX.