Homework 6

1. Write a function that finds the MLE estimates for parameters of the beta family. The function should take a data vector and starting values as inputs. It should return error messages if starting values or any data points belong to innapropriate ranges. Do not use built in functions in R or Python to complete this homework.
2. Use the code from the previous problem you wrote to perform a simulation study on how sample size affects MLE estimates. Estimate the bias and variance for the MLE estimate of data arising from a beta(2,4) distribution using sample sizes ranging of 15, 30, 100, and 1000.
3. Use the code from the previous problems to write a function that will inout data and starting values and return a bootstrap confidence interval for the MLE estimates of each of the beta parameters. Use Ted William's Batting averages by year for his entire career. These can be found in the table under BA at Ted Williams
4. Submit this homework by committing the necessary files (including any data files) in the appropriate directory and pushing to your central Git repository. Remember to not commit files that are easily reproducible.