class: center, middle, inverse, title-slide # Bayes’ Rule for Random Variables Review ### Dr. Dogucu --- layout: true <div class="my-header"></div> <div class="my-footer"> From Bayes Rules! book Copyright © Drs. Alicia Johnson, Miles Ott & Mine Dogucu. <a href="https://creativecommons.org/licenses/by-nc-sa/4.0/">CC BY-NC-SA 4.0</a></div> --- ## 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 `\(\pi\)`.