(10 points) In probability theory and statistics, the gamma distribution is a two- parameter family of continuous probability distributions. The exponential distribu- tion, Erlang distribution, and chi-square distribution are special cases of the gamma distribution. The PDF of the distribution is in the form of 1 f (x; k, 0) = T(k) OK 20 0 , x 2 0, where I(k) = (k - 1)! is a gamma function. Find the maximum likelihood estimate (MLE) for Gamma distribution's parameter 0. Please make sure to complete details of the derivations