Although the system of equations (6) can be solved directly, we have chosen to solve (3) using optimization software, and then use (6) to verify that the optimality conditions are met. Consider again the example from Mood et al. (1974) presented in Figures 1 and 2. We desire a 95% confidence interval on θ, the probability of a success. Note that the point estimate θ ̂ for this problem is .2