Assume I feel that my prior experience concerning the relative frequency of smokers in a particular bar is equivalent to having seen 14 smokers and 6 nonsmokers. So I represent my beliefs concerning the relative frequency of smokers using the density function. Suppose I then decide to log whether or not individuals smoke. Compute the probability of getting the data
where 1 means the individual smokes and 2 means the individual does not smoke.
Assuming the beliefs in exercise a), what is the probability that the first individual sampled smokes? If we obtain the data shown in that exercise, what is the updated beta density function representing my updated belief concerning the relative frequency of smokers? What is the probability that the next individual sampled smokes?