The following problem is motivated from the paper by Brown (2008). "Batting average is one of the principle performance measures for an individual baseball player. It is the percentage of successful attempts, Hits, as a proportion of the total number of qualifying attempts, At- Bats. In symbols, the batting average of the ith player may be written as BAi = Hi/ABi. This situation, with Hits as a number of successes within a qualifying number of attempts, makes it natural to statistically model each player's batting average as a binomial variable outcome, with a given value of ABi and a true (but unknown) value of pi that represents the player's latent ability." "We will look at batting records for each Major League player over the course of a single season (around 6 months). We use the batting records from the first half of the season (e.g., the first 3 months) in order to estimate the batter's latent ability, pi, and consequently, to predict their BA performance for the remainder of the season. Since we are using a season that has already concluded, we can then validate the performance of our estimator by comparing the predicted values to the actual values for