In Question 9 of the activities, you were shown a possible prior distribution for the proportion of brown or orange M&€™s given in Table 11.2. Now consider another prior distribution for Ï€, displayed in Table 11.8, that allows for four possible values of Ï€.
a. Compute the prior estimate of π, E(π), and the prior variance, Var(π).
b. Using your M&M€™s data or the MyMMs data, compute the posterior distribution for p.
c. Compute the posterior estimate, p*, and the posterior variance, Var(Ï€ | x).
d. Comment on the differences between the prior and posterior distributions for π. Include statements addressing the center and spread of the distributions.
Table 11.8

Transcribed Image Text:

π | 0.25 | 0.30 | 0.35 | 0.40 p(π)|18 138 |38 | 1/8