By <Bayes theorem>, with respect to Lebesgue measure on $(0,1)^2$,
$$
\boxed{
\pi(\lambda,\rho_G\mid y_G)
\propto
(\lambda\rho_G)^{y_G}(1-\lambda\rho_G)^{N-y_G}
\rho_G^{a-1}(1-\rho_G)^{b-1}.}
$$
The omitted constant includes the <binomial coefficient> and the normalizing constant of the <Beta distribution>; the uniform prior contributes only the support indicator.

Solution

Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 207 / 1 / d / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2019/iii/paper-207/1/d/solution