3.4. [This problem is loosely based on examples from Chap. 4 of Albert (1997). You are the assistant coach of the women's softball team at a Midwestern college. The head coach has asked you to assess a new first year player who is joining the team. As a high school student, she was at bat 120 times and got 40 hits. You wish to estimate e, her underlying true probability of getting a hit in any at bat as a college-level player. 1. Specify a beta prior that seems appropriate to capture your knowledge or uncertainty about before the new player plays in any college-level games. Use any information you have that seems importanther high school record, anything you know about college-level women's softball, etc. Use R functions as needed. Explain in a few sentences (supplemented with plots and/or R output) how you chose the values of a and B. There is no one right answer hereI want to see how you think about this and what procedure you use. 2. Specify a beta prior that you think might reflect the player's mother's beliefs about . This may be similar to, or quite different from your prior. Again, justify your choice with graphical or numeric R output. 3. Suppose the player now plays eight college-level games, has thirty at bats, and gets 5 hits. Thus, the data are y=5, n=30 We will use a binomial likelihood for these data. This requires the assumption that, conditional on e, each at bat is an independent Bernoulli trial with success probability . There are several reasons why independence might actually not be a reasonable assumption in this problem. Give one. Note: For our present purposes, we'll use a binomial likelihood anyway. We'll come up with a better model when we talk about hierarchical models later in the semester. 3.4. [This problem is loosely based on examples from Chap. 4 of Albert (1997). You are the assistant coach of the women's softball team at a Midwestern college. The head coach has asked you to assess a new first year player who is joining the team. As a high school student, she was at bat 120 times and got 40 hits. You wish to estimate e, her underlying true probability of getting a hit in any at bat as a college-level player. 1. Specify a beta prior that seems appropriate to capture your knowledge or uncertainty about before the new player plays in any college-level games. Use any information you have that seems importanther high school record, anything you know about college-level women's softball, etc. Use R functions as needed. Explain in a few sentences (supplemented with plots and/or R output) how you chose the values of a and B. There is no one right answer hereI want to see how you think about this and what procedure you use. 2. Specify a beta prior that you think might reflect the player's mother's beliefs about . This may be similar to, or quite different from your prior. Again, justify your choice with graphical or numeric R output. 3. Suppose the player now plays eight college-level games, has thirty at bats, and gets 5 hits. Thus, the data are y=5, n=30 We will use a binomial likelihood for these data. This requires the assumption that, conditional on e, each at bat is an independent Bernoulli trial with success probability . There are several reasons why independence might actually not be a reasonable assumption in this problem. Give one. Note: For our present purposes, we'll use a binomial likelihood anyway. We'll come up with a better model when we talk about hierarchical models later in the semester