Now my grading is over, I can reflect on the unexpected difficulties in the mathematical statistics exam. I knew that the first question in the multiple choice exercise, borrowed from Cross Validation, was going to be quasi-impossible and indeed only one student out of 118 managed to find the right solution. More surprisingly, most students did not manage to solve the (absence of) MLE when observing that n unobserved exponential Exp(λ) were larger than a fixed bound δ. I was also amazed that they did poorly on a N(0,σ²) setup, failing to see that
and determine an unbiased estimator that can be improved by Rao-Blackwellisation. No student reached the conditioning part. And a rather frequent mistake more understandable due to the limited exposure they had to Bayesian statistics: many confused parameter λ with observation x in the prior, writing
hence could not derive a proper posterior.