Problem 1: Suppose that X follows a geometric distribution: P(X = k) = p(1-p)k-1 and assume a random sample X₁, X₂, ..., Xn. a) Find the method of moments estimator of

p. b) Find the MLE of p. c) Find the maximum likelihood estimate of p if the collected sample dataset is {1, 5, f9461a1a151a4ff3b37288fe3df325d7-1_1706742943624.pdf 1, 2, 6, 2, 3, 7, 3, 8).