For 10 coins, let i denote the probability of a head for coin i. You flip each
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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 of πi. Formulate a model for which these are the ML estimates.
b. Formulate a random effects model for the data. Using software, obtain predicted values {πˆi}.
c. Suppose all πi = 0.50. Compare the estimates in
(a) and in
(b) by finding the average absolute distance of the estimates from 0.50 in each case. What does this suggest?
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