Model the horse kick deaths using the Poisson distribution with different parameters for each of the corps. Learn Poisson distribution parameters for each of the corps using first 13 years of data and make predictions on remaining 7 years and compute the RMSE of predictions for each of the corps.

1. Use maximum likelihood estimation to learn the parameters.
2. Use maximum aposteriori estimation to learn the parameters a. Assume appropriate prior distribution over parameters and justify your assumption b. Plot prior, likelihood and posterior and provide your observations in terms of mode of the distributions for corps 2, 4 and 6.