For 10 coins, let πi denote the probability of a head for coin i. You flip each coin 5 times. The sample numbers of heads are (2, 4, 1, 3, 3, 5, 4, 2, 3, 1). a. Report the sample proportion estimates...

Explanation:
EXPLANATION 1:
· The sample proportion estimates of πi are 0.40, 0.80, 0.20, 0.60, and 0.60. The model for which these are the ML estimates is a binomial model with n = 5 and p = 0.5. 
· This model is a good fit for the data because it is able to estimate the probabilities of each coin accurately. 
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EXPLANATION 2:
· The random effects model for the data is a binomial model with n = 5 and p = 0.5. The predicted values {πˆi} are 0.50, 0.50, 0.50, 0.50, and 0.50. 
· This model is not a good fit for the data because it does not accurately estimate the probabilities of each coin. 
EXPLANATION 3:
· The estimates in (a) are closer to 0.50 than the estimates in (b). This suggests that the binomial model with n = 5 and p = 0.5 is a better model for the...