7.26 For the model of Exercise 7.25, suppose that the total number infected, i, occurs with frequency Xi, i = 1, 2, 3. Obtain the expected Fisher information. Write down the asymptotic distribution of the maximum-likelihood estimator ˆθ, and use it to obtain an approximate 99.5% confidence interval for θ when X1 = 6, X2 = 11, X3 = 13 and ˆθ = 0.4765. Compare this interval with that resulting from taking an appropriate section of the log-likelihood.

In standard notation, an iterative procedure for evaluating ˆθ proceeds according to the iteration: