Fit a binomial regression model to the O-rings data from the Challenger disaster, using a complementary log-log link. You must use R (but without using the glm function); I want you to work from first principles. (a) Compute MLEs (maximum likelihood estimates) of the parameters in the model. (b) Compute 95\% CIs for the estimates of the parameters. You should show how you derived the fisher information. (c) Perform a likelihood ratio test for the significance of the temperature coefficient. (d) Compute an estimate of the probability of damage when the temperature equals 31 Fahrenheit (your estimate should come with a 95\% CI, as all good estimates do). (e) Make a plot comparing the fitted complementary log-log model to the fitted logit model. To obtain the fitted logit model, you are allowed to use the glm function.