Problem 1. The geometric distribution is often used to describe the number of 'trials' it takes before we see a 'success', where each trial is i.I.d. Bernoulli(p). Consider a sample {X1, X2, ...,x,] of i.i.d. draws from the geometric distribution, which has pdf f(x;p) = (1-p)*-ip . a) Write down the log likelihood function for the sample. b) Show that the MLE for p isp = /x