Let's say that we work for the International Olympic Committee (IOC) as part of their Fight Against Doping. We have a drug test for a banned performance-enhancing drug (PED) that is 99.3% accurate at identifying the presence of the PED in an athlete's system. However, it is only 73% accurate at identifying the absence of PED in the athlete's system. From a scientific study we also have a strong a priori reason to believe that only 3% of Olympic athletes use this particular PED.

1. Our information that only 3% of Olympic athletes use the PED came from a study of 300 athletes. This year we tested 500 athletes and confirmed that 11 of them used the banned substance. In both cases, only a sample of all athletes to complete in the Olympics were tested for the PED. As a result there is some uncertainty, so we decide we would like to express what we have learned as a beta distribution. In two years when we being testing athletes again, what is our updated prior distribution for the percentage of Olympic athletes using the PED?

I am having trouble figuring out the answer to this question above. I know that the answer to the question is not a plot, it is the beta distribution written out in terms of its parameters. For example, the parameters of the normal distribution are the mean and variance, so we write it asN(,2 ).