For 10 coins, let i 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)

1. (a)If we are interested in estimating i, does it make more sense to use a GEE or a GLMM for this model?
2. (b)Fit a random effects model to this data and obtain predicted values {i}
3. (c)Make a plot to compare the predicted probabilities from (b) and the sample proportions.
4. What do you see?
5. (d)Suppose now that the true values are i = 0.5 for all i. Calculate the mean squared error of your estimates as well as for the sample proportions. The mean squared error is calculated as the average squared difference between your estimate and the truth.