Suppose a different analyst considering the data in Example 6.2 concludes that a reasonable prior distribution for the binomial p in this situation is Gaussian, with mean 2/3 and standard deviation...

Suppose a different analyst considering the data in Example 6.2 concludes that a reasonable prior distribution for the binomial p in this situation is Gaussian, with mean 2/3 and standard deviation

1/10.

a. Find the parameters of a beta distribution that approximates this Gaussian prior distribution.

b. Using the results of part (a), find the posterior distribution for p.

c. Find the resulting predictive distribution for the number of “successes” in the next N⁺
= 5 independent observations. (Use a computer to calculate the logs of the gamma function.)