Ignoring factors that do not depend on the parameters, the product of the two <binomial likelihoods> is
$$
L(\phi_0,\phi_1)
=\phi_0^{120}(1-\phi_0)^{80}
 \phi_1^{110}(1-\phi_1)^{110}.
$$
Including the sampling constants multiplies this by ${200\choose120}{220\choose110}$.

Solution

Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 207 / 2 / 1 / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/iii/paper-207/2/1/solution