******Please use R studio*****************************

Question 9 Here we apply Bayesian inferenoe to an everyday problem. Suppose we have a coin and are not sure if it is a fair coin or a doubleheaded coin. The two hypotheses would be Hf: p{H) = 0.5 and Hg: p(H) = 1. Our priors would be p(Hy} = 0.999., 30in) = 0.001 and our data would be 6 successive heads. - Apply Bayes's theorem to calculate the posterior probabilities for H y and Hg. - With these priors, how many heads would you need to observe to take your posterior probability for Ed to exceed 0.5? - (harder) Compare the results with a conventional frequentist analysis. . Give an example of Bayes's theorem in your everyday life. State 2 or 3 hypothesis clearly. state your priors clearly, state your data clearly, state your likelihoods clearly and apply Bayes's theorem to your situation. Comment briey on whether Bayesian logic is operating as expected in this situation