Describe your model including the likelihood and prior.

1. The data set NBAclutchFT.csv (Week #4 Course Content on D2L) has the overall free throw proportion and results of free throws taken in pressure situations, defined as “clutch”, for ten National Basketball Association players (ten out of the top eleven players that received the most votes for the Most Valuable Player award) for the 2020-2021 season. Since the overall proportion is computed using a large sample size, assume it is fixed and analyze the clutch data for each player separately using Bayesian methods

(a) Describe your model including the likelihood and prior.

(b) Plot the posteriors of the clutch success probabilities.

(c) Summarize the posteriors in a table.

(d) Test the hypothesis that the clutch proportion is less than the overall proportion.

(e) Are the results sensitive to your prior?

2. Say that Y|θ ~ Binomial(N,θ) and Z|θ~Binomial(M,θ), and that Y and Z are independent given θ. Identify a conjugate prior for θ and find the corresponding posterior distribution.