One of the requirements of some Ph.D. statistics programs is a comprehensive exam. Our summer intern took her comprehensive exams in statistics for the University of Illinois last summer, but we didn't find out any of the questions.
But Radford Neal is posting past questions he's posed on comprehensive exams at the University of Toronto on his blog.
Try your luck at #1. After you've thought it through, see Radford's answer here.
Now Radford's posted #2, but not posted the answer yet.
My degree is in social psychology, not statistics, but a good portion of my comprehensive exam dealt with Bayesian/Baysean/Bayesean issues. Yes, readers, I spelled that common statistical term 3 different ways on these questions.