In a COVID vaccine trial, no subjects were given a placebo and n1 were given the vaccine; x0 of the placebo subjects developed the disease and x1 of the vaccinated subjects. Considering the pro bability model Xk~Binomial(nk, pk), the vaccine efficacy is defined to be e = (1-p1 )/p0. (1) State the maximum likelihood estimators for p and p1. Give a formula for the maximum likelihood estimator for e. (ii) Explain how to compute a 95% confidence interval for e. Also explain how to test whether e >0.5