Consider the geometric distribution, which has P(X = k) = (1 ) k1 . Assume in our training data X took on the values

Consider the geometric distribution, which has P(X = k) = (1 − θ)^k−1 θ. Assume in our training data X took on the values 4, 2, 7, and 9. 

a. Write an expression for the log-likelihood of the data as a function of the parameter θ. 

b. What is the value of θ that maximizes the log-likelihood, i.e., what is the maximum likelihood estimate for θ?