3.3∗ (Brooks et al., 1997.) The data below describe the number of dead fetuses in litters of mice. Use the Matlab routine fminsearch to fit the beta binomial model, which has the probability function:

pr(X = x) =

*n x

+ x−1 r=0 (μ + rθ)

n−x−1 r=0 (1 − μ + rθ)

n−1 r=0 (1 + rθ) ,

= Q(x, n, θ), say, for 0 ≤ x ≤ n, where n denotes the number of fetuses, and X is the number that die.

(See Exercise 2.7.) Also shown are the expected values resulting from the maximum-likelihood estimates, ˆμ and ˆθ.