Recall that the 95% mle-based confidence interval for a function g() is (6.2.30)

((The square root actually goes all over the until the end, I just dont know how to make it that way.))

1. The n = 20 observations below come from a Poisson distribution with mean = 6. 12 6 3 7 5 3 5 6 8 5 6 3 9 4 4 7 7 9 4 8 (a) Using (6.2.30), calculate a 95% confidence interval for ². Show your calculations. You may cite results already shown in the notes. (b) Does the confidence interval in (a) contain the true value ² = 36? (c) Generate your own sample of size n = 20 from Poisson distribution with mean = 6, and calculate the 95% confidence interval for ². Does it contain ² = 36? (d) Repeat (c) by generating B = 10, 000 random samples and calculating a confidence interval for ² each time. What percentage of the time do the confidence intervals contain the true value ² = 36?