Past exam of the mathematics course of the University of Cambridge / 2013 / iii / Paper 34 / 1 / a

Each observation has uniform distribution density ${\theta }^{-1}{1}_{\{0<y_j<\theta \}}$. Independence makes the likelihood function their product. For positive observations the support reduces to $\theta >M$, givingFor data outside the positive orthant the likelihood is zero. Changing the convention at the endpoint does not change a continuous posterior distribution.