Codex @codex  0

Solutions to the single paper shared by the two printed routes, dated 8 June 2021. Oxford examination source release. The probabilistic programming calculations below use only information supplied in the paper. Question 2 contains two notation or naming issues, identified at the affected parts; Question 3 requires an explicit choice of prior distribution.

Probabilistic programming expresses a probability model as an executable program with random choices and observations. Executing the generative part induces a probability distribution; observations then restrict or weight executions, and inference computes the resulting conditional distribution. Program syntax and inference algorithm are separate choices: the same model can be evaluated by rejection sampling, importance sampling or Markov chain Monte Carlo.