Exercise

Let proportion of women in the U.S. who develop breast cancer in their lifetime be $\pi$. Even though $\pi$ can take any value between 0 and 1, for the purposes of this question, we will assume possible values of $\pi$ as 0.05, 0.10, 0.30, and 0.50. Since we do not have any medical doctors in our class, we will pretend that we do not have any specific prior ideas about breast cancer and choose a uniform prior. We look at medical records of 8 women who have passed and 1 of them had developed breast cancer at some point in their life. Calculate the posterior distribution for $\pi$.