g We have a (synthetic) dataset of 1000 days of positive precipitation in measured in NYC in mm, attached in the rain. npy file. In this question we will work through modeling this data analytically and numerically, and simulating new data to determine risks for the city. a) The Likelihood Function Assuming a Gamma distribution, write down the likelihood and log likelihood functions of the shape and scale parameters. Solve for the MLE of the shape and scale parameters. You can leave your answer for the shape parameter in terms of the Digamma function.