Measuring model complexity is a tricky business. Two well-known (and related) measures of model complexity from statistics are the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC). Find and read a little about the definitions of AIC and BIC. (a) Suppose you are reading a research paper that lists the AIC and BIC for a model trained on a dataset with 1000 training points. You would like to determine the maximum value of the likelihood. If AIC = 20003.2189 and BIC = 69080.7717, what is the maximum value of the likelihood to four decimal places, and how many parameters does the model have? (b) Produce a 3D plot of AIC for suitable ranges of L and k, where L is the maximum value of the likelihood function for the model and k is the number of parameters in the model.