Exercises for Wed 1 October

1. On Wed Sept 24 I discussed most of the material of Ch 5 relating to the CLT (the central limit theorem), the LLN (the law of large numbers), convergence in distritbution. We also had our first "extra lecture" 13:15 to 14:00 with more time for exercises and details; there will be a second such in perhaps three weeks time. Next week I shall first round off Ch 5, with the delta method, before starting Ch 6.

2. I ought to have a clear and detailed curriculum list ready by next week. Note that Section 5.6, on simulation, will not be inside the "active curriculum" part.

3. My PhD student Gudmund Hermansen defends his thesis Friday September 26, and his open trial lecture, on the topic given to him by the committee, namely "Dimensionality reduction in big data sets", takes place in Auditorium 5. This is related to Ch 6, so perhaps I will invent exam questions from this lecture.

4. Exercises for Wed Oct 1: From Ch 5, do #30, 31, 32, 44, and find out what on earth is going on with #58. Extra A: For a sample of n data points from the uniform on (0,1), find the limit distribution of sqrt(n)*(M_n - 1/2), where M_n is the median, by working with its probability density. Take for simplicity n to be odd, say n = 2m + 1. Generalise to an arbitrary smooth distribution. Extra B: Prove Slutsky's Theorem, 5.5.17(a) in the book, first for a = 0, then for a nonzero.