Please use Rstudio

Question 5 Consider an experiment which may either succeed or fail with probability p, where p is unknown. Trials are independent of one another. An expert has a prior PDF for p which is a beta distribution with o = 1.3, 8 = 1.5; the experiment is performed 5 times with 3 successes and 2 failures. . Plot the prior and posterior PDFs. . Calculate the maximum likelihood estimate for p, and give the prior mode . Calculate the posterior mean . (harder) give a Bayesian credible interval, that is, two values pr, pu (for lower and upper, respectively), such that Probposterior (p > PL; P