Homework 1: Due Wed Oct 8:
Reading: Lehmann and Casella, TPE, pages 1-16.
Wellner lecture notes Chapter 0 (skim only)
Exercises:
Numbers 1,2,3,4 of
Wellner Problem set 1
Here are JAW solutions to problem set 1.
Homework 2: Due Wed Oct 15:
Reading: TPE Pp. 16-45 ; JAW Chapter 1, Pp 6-7 and 13-17.
Exercises:
1. 1 (a) and 1 (c) of
JAW Problem set 2 .
Use the defn of non-central chisquared as Poisson mixture of Gammas
2. (a), (b), (c): Ferg, Pp 6-7: Nos. 3(a), 4, 5 resp.
(qm is "quadratic mean")
3. Number 4 of
JAW Problem set 2
4. TPE P.65 No. 4.3
5. TPE P.65 No. 4.13
6. TPE P.69 No. 6.7
Homework 3: Due Wed Oct 22:
Reading: Ferguson sections 1 and 2; JAW notes Chapter 2, Pp 3-8, 13.
Exercises:
1. (a) Prove the Cauchy-Schwarz inequality directly (i.e. don't just cite
Holder).
(b) JAW Lecture notes: Exercise 1.2 on P 2.7
2. JAW lecture notes: Exercise 1.3 on P. 2.7-8
3. (i) Ferg. P.12 #4(b) (You will a.s. need to look at the solution
if you have not seen this before.)
(ii) Ferg. P.11 #1 (both (a) and (b))
4. Number 5(a) and 5(c) of
JAW Problem set 2
(The answer to (b) is "no" which is what makes (c) interesting.)
5. and 6. are here
Here are JAW solutions to problem set 2.
Homework 4: Due Wed Oct 29:
Reading: Ferguson sections 3 and 4.
Exercises are here.
Wed Nov 5: no homework due
Homework 5: Due Wed Nov 12:
Reading:Ferguson sections 5 and 6; TPE Pp 113-129.
(Let's declare this final: 10/31)
Numbers 1,2,3 are here.
(In number 1: you may find it easier to think about the particular
case (d) before doing (b) and (c); you may assume a(theta) and
b(theta) are strictly increasiong/decreasing.)
4. (a) Ferguson P. 24, # 2
(b) Ferguson P. 42 #3
5. (a) TPE P. 139 No. 5.17
(b) TPE P.140 No. 5.18
Homework 6: Due Wed Nov 19:
Reading:TPE Pp.437-455
Exercises are here.
Typo in #5 -- no abs in defn of T_n.
Homework 7: Due Wed Nov 26:
Reading:TPE Pp.461-475
Exercises are here.
In No 2: For large n, (NOT large rho, which would make no sense).
In 3(b): you may assume 0 lt p lt 1
In 3(c): to get a non-degenerate limit, r and s have to increase with
n -- take r=np, s=nq (approx), for example, 0 lt p lt q lt 1.
In 3(d): you need not use 3(a) -- it is easier to use the density of
all the U_(i) directly. If you do use the form in terms of the
exponentials, you will want to use the version conditioned on
fixed W_{n+1}
In 5(b), delete ``at x=theta'' -- in earlier version.
Homework 8: Due Wed Dec 3:
Reading: None -- it is THANKSGIVING
Exercises are here.
In 2(c)
As you will know: sum_1^n i^2 = n(n+1)(2n+1)/6
In 4 (a), (b), (c): the second compoment of beta should be nu, not mu
(mu is gone since we are assuming mu=lambda)
Homework 9: Due Wed Dec 10:
Reading: TPE Pp 456-460 (well it's not that useful actually)
Exercises are here.
As always, please let me know of typos.
Note this homework has two pages -- not because it is long, but
because it tells you all the details!