Examples Sheet 1 I supervise 21 students. Here is some feedback from the first example sheet, in case you are interested. 1. None of them realised that it ought to be explained why in (d) the estimator could be taken to be a function of T. [Think about sufficient statistics.] 2. A minor niggle -- 3/4 of them wrote out probabilities for GG,Gg,gg which didn't sum to 1, not realising that Gg=gG. 3. Fine 4. Fine, except that many couldn't work out E(1/T) in part (c). 5. (a) Only 1 or 2 realised the point of the hint -- the rest just worked out dp/dtheta. (b) Over half just didn't see how they could find an unbiased estimater, despite the hint. Several even came up with estimators which were functions of the parameter they were trying to estimate. 6. Answered better than 5 was. A few just didn't think of Rao-Blackwell, but those who did answered well enough. They were helped by the similar example in the lecture, but many didn't really understand it -- they just copied it out. 7. Most answers were laborious. They tried to construct confidence intervals, rather than just working out the probability of the one that was given. But at least there was only one student who didn't understand that it is the interval which is random. 8. A quarter of them simply had no idea what to do, to show that S and C are 95% confidence intervals. Most realised that it is sensible to choose a smaller confidence interval, but three or four said they would prefer S because it is _bigger_. 9. Most just blithely followed the example in the lectures. But those that stopped to think had trouble working out why the data was interpreted in the way it was. Surprisingly, more than half had trouble with finding a point estimate and relating it to maximum likelihood. They were not persistent enough to just calculate the expected loss. 10. All OK 11-13. Only one of them used indicator functions in a sensible way in question 11; most got bogged down. All of them left their constants in far too much, and some even tried to work out integrals. I had to stress: ignore constants, and think of the expression you end up with as a _distribution_, not just a function which has to be integrated. There was a general consensus that the lectures were enjoyable and that printed handouts were good :-)