Penn State is interested in estimating p, the proportion ofstudents who developed COVID after being vaccinated during thespring semester of 2021 before students were required to bevaccinated. A random sample of students all of whom reported havingCOVID was obtained and recorded as (X1, X2, …, Xn) where eachstudent in the sample was classified as Xi=1 if the student wasvaccinated prior to developing COVID, and Xi=0, if not.

a. Write the likelihood function a frequentist would use toestimate p for the data set. The Study Lead took a Bayesianapproach and chose the following non-informative prior on p where?(p) = 1/(p(1-p) ) for 0 < p < 1 .

b. Write the posterior distribution ?(p|(X1, X2, …, Xn)) to beused for this Bayesian approach.

c. A 95% credible interval was computed by the Study Lead to beequal to (0.01, 0.03). Write an interpretation using 1 or 2sentences of this credible interval that Penn State can use toreport the results to the general Rutgers population.