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3.1 The binomial distribution

3.1.1 Conjugate prior

In this section, the parameter of interest is the probability π of success in a number of trials which can result in success (S) or failure (F), the trials being independent of one another and having the same probability of success. Suppose that there is a fixed number of n trials, so that you have an observation x (the number of successes) such that

from a binomial distribution of index n and parameter π, and so

The binomial distribution was introduced in Section 1.3 on ‘Random Variables’ and its properties are of course summarized in Appendix A.

If your prior for π has the form

that is, if

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