exercises for Week 2, Aug 26 to Aug 30

The plan is to use *a bit less than 5 weeks* for Chs 1, 2, then about 2 weeks for each of Chs 3, 4, 5. If things go well, we round off Ch1 on Mon Sept 2 and start on Ch2 Thu Sept 5.

Ch 1 has a multitude of exercises, of which we might be defining about a total of 25 as curriculum. After as much as we muster in Week 1 of 1, 2, 3, 4, 7, 8, 9, 10, 12, 15, 16, we go for

17, 18, 21, 23, 24, 29, 30, 31, 33, 

then the last batch with 40, 41, 43, 45, 49, 50. 

(a) For Week 2, Monday, Aslak H does 1.12(e), Maham I does 1.17, on the blackboard; for Thursday, David S does 1.30(c),(d),(e).

(b) I pointed to a somewhat heavy-handed way today Mon Aug 26 to find prodd and preven for the Poisson; it works, but an easier way is this. Write down power series sums for prodd and preven, with prodd + preven = 1. Show that preven - prodd = \exp(-2\theta), then show preven = \half(1 + \exp(-2\theta)), prodd = \half(1 - \exp(-2\theta)). 

(c) I liked, and admit being a bit surprised, by the result of 1.16(e), kicking my ball towards the long line in this moderately strange fashion to get a normal X out of it. If anyone has additional results or insights, report to us. What does the angles density g_\nu(a) need to be, in order for the resulting X to be a t_\nu? Check how the densities look like, for \nu big and \nu small.

In a while we also go into the Statistical Stories.

Footnote: Exercise 1.16(e) kaster nytt lys over Handke-debatten.
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