For a group of 100 randomly chosen people, compute: (a) the expected number of days of the year which are birthdays of exactly two people.(b) the expected number of days in the year which arenotbirthdays of anyone.(c) the expected number of days in the year which are birthdays of someone in the group.(d) let x be a geometric random variable with pdf: p(x=k) = qk−1p, k= 1,2,3, . ..prove that the moment-generating function of x is m(t) = pet / (1−qet), t < −logq. can you explain why m(t) does not exist if t≥ −logq?