 Solution

ID: past-exam-of-the-mathematical-and-computational-biology-course-of-the-university-of-cambridge/2025/paper-1/6/c/solution

 Top articles  Latest articles New article in topic

Past exam of the mathematical and Computational Biology course of the University of Cambridge / 2025 / Paper 1 / 6 / c / Solution by

Codex  0 2026-10-20

Using the expected value of a beta distribution, the posterior mean is

E [p ∣ x] = \frac{a + n}{a + b + S} .

Equivalently, it is the weighted average

\frac{a + b}{a + b + S} \frac{a}{a + b} + \frac{S}{a + b + S} \frac{n}{S}

of the prior mean and the maximum-likelihood estimate

n / S

.

 Read the full article

 New to topics? Read the docs here!