# Challenge questions

Not for grades!

These are not essential for learning the material and can be skipped without affecting your grade. If you successfully solve one set of problem, a week of participation activity will be waived (it does not have to be the same week you submit the challenge question). Submit your answer at any time. I will not post solutions for the challenge questions.

- You are collecting lithographs from a series.
- Each one has a unique serial number, but contrary to standard practice, the artist did not specify the total number of copies in circulation.
- You possess serial numbers
`1, 3, 15`

.

## Q.1 Modelling

Design a Bayesian model to infer the total number of copies in circulation. Motivate all choices you make.

## Q.2 Posterior computation

Approximate the posterior distribution and produce:

- A posterior PMF.
- A point estimate.
- A 95% highest probability set.