The file Vinnie-Johnson.txt provides data on the shooting of Vinnie Johnson of the Detroit Pistons during the 1985-1986 through 1988-1989 seasons. Source was the New 1 York Times. The data were analyzed in the Carnegie Mellon Ph.D. Thesis of Kate Hsiao and some results are cited in Example 2 of Kass, R.E. and Raftery, A.E. (1995), Bayes Factors, J. Amer. Statist. Assoc., 773-795. The first column is the year, with 85 indicating 1985, etc.. The second column is Field Goals, the third column is Field Goal Attempts. Assume that yij ind Bin ( nij , i ) , where yij is the number of Field Goals and nij is the number of Field Goal Attempts in the jth match in the ith year with i = 1 indicating year 1985, i = 2 indicating year 1986, and so on. There are a total of 380 games in the data set. Suppose that a priori 1, . . . , 4 are 4 independent beta random variables with parameters 1/2 and 1/2. (a) Find the prior means and prior variances of 1, . . . , 4. (b) Find the posterior distribution. (c) Find the posterior means and posterior variances