On a particular examination paper, a pupil whose mean score is μ
will actually score X, where X has a U(μ − 10, μ + 10) distribution.
Over the pupils taking the test, μ is assumed to have a U(10, 90)
distribution. Find the density of the test score of a randomly chosen
pupil.
Given that Fred has scored x, what is the distribution of his underlying mean score?