See below:

Question 9 Consider a sample X1; X2; ...; Xn of independent and identically dis- tributed random variables, where for each i, X, has a geometric distribution 72 with probability mass function f(x, 0) = Prob(X, = x} = 0(1 -0)3-1, Vre {1;2;3;...} where the success probability 0 satisfies 0