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 :-)