Note that doing only the Homework examples is likely insufficient to gain practice and understanding. One learns by doing examples: this is true of all Math, but especially true of Probability and Ststistics. Examples other than the homework may be suggested on the schedule. The TA, Nick Basch will be doing many examples with you; usually in the Monday class.
Note also the information regarding homeworks on the
Class home page.
Homeworks are only final at 11.30 a.m. on Wednesdays, ONE WEEK before homework is due. Up to that time, changes may be made. After that time, only ESSENTIAL changes will be made, and every effort will be made to inform students, usually via the class email.
Homework 1; Due 11.30 a.m. Wed January 13
LM: 2.2.22 (p31), 2.4.11 (p52), 2.4.28 (p61), 2.5.25 (p.85),
3.2.5 (p137), 3.2.19 (p147).
These are all examples that should be review.
The last three are review of geometric, binomial, and hypergeometric probabilities.
Homework 2; Due 11.30 a.m. Wed January 20
LM: 3.5.4, 3.5.7, 3.6.9, 3.6.12, 5.4.9, 5.4.18
The first four review expectations and variances.
The last two apply expectations and variances to ideas of estimation.
5.4.9: hint: first find E(Y).
Homework 3; Due 11.30 a.m. Wed January 27
LM 5.2.16 (P362): 5.2.23 (P.363): 5.4.2, 5.4.7, 5.4.10, (P.387); 5.7.2 (P.409)
P. 362; 5.2.16: Hint compute E(Y)
P. 363; 5.2.23: Look up formulas for E(X) and E(X^2).
P. 409; 5.7.2: You may assume E(Y^4) is finite for a Normal distribution.
Homework 4; Due 11.30 a.m. Friday, February 5
LM: 4.2.10 (P287), 4.2.26 (P292), 4.3.10 (P301),
3.12.5 (not (a)) (P261), 3.12.14 (P.266), 4.6.1 (P.332)
The first three review Poisson probabilities and processes,
and normal approximations for Binomial.
The next two are about mgfs, and the last is about a Gamma r.v.
4.3.10: Use a continuity correction in (b): See Pp 296-7
3.12.5: do only parts (b), (c) and (d) -- we did not do (a) yet.
Homework 5; Due 11.30 a.m. Wed Feb 10
Homework 6; Due 11.30 a.m. Wed Feb 17
Homework 7; Due 11.30 a.m. Friday, February 26
Homework 8; Due 11.30 a.m. Wed Mar 3
Homework 9; Due 11.30 a.m. Friday Mar 12
This is a half-homework-- for grading it will likely be paired with another
half-homework later in the quarter
LM: 3.7.11 (P210); 3.7.22 (P213); 3.7.44 (P219).
LM: Pp 355-357; 5.2.4, 5.2.6, 5.2.9, 5.2.11, 5.2.12, 5.2.14
Note: If you differentiate the log-likelihood and find a single
solution for the MLE you do not need to differentiate again
to show it is a maximum.
PDF copy of hwk 6 questions
Note; this is due on the FRIDAY after the midterm. However, it is
strongly recommended that you look at 5.6.1 and 5.6.5 BEFORE the
midterm.
LM: P. 405; 5.6.1, 5.6.2, 5.6.5 (These are on Sufficiency)
LM: P. 397; 5.5.2, 5.5.3, 5.5.4 (These are on efficiency)
PDF copy of hwk 7 questions
This is a half-homework-- for grading it will paired with Hwk 5.
LM: P 376-379: 5.3.1, 5.3.10. 5.3.23.
PDF copy of hwk 8 questions
LM: P 422-423; 5.8.1, 5.8.4, 5.8.5, 5.8.6, 5.8.7, 5.8.8
PDF copy of hwk 9 questions
Note: for these questions you will need to know that a beta pdf is
proportional to x^(r-1).(1-x)^(s-1) on x in (0,1), and its mean is
r/(s+r).
5.8.4: It is very bad terminology to call this an ``uninformative'' prior
-- we may talk about why in class. However, otherwise, this question is good.
Suppose the data is the outcome of
a single Binomial(n, theta) random variable.
For squared-error loss, the estimate is the posterior mean -- we will learn
that in class, but maybe not until Wed mar 10.
5.8.5: Do only for the case 5.8.4. Again this terminology is VERY bad.
What LM means is to consider the estimator which is the random variable of
which your Bayes estimate is the outcome, and then see whether this estimator
is unbiased/asymptotically-unbiased (in the regular non-Bayesian sense).
5.8.7: In the book's terminology W is the sufficient summary statistic, and
we need to find the posterior pdf for theta given W=w.
5.8.8:
For squared-error loss, the estimate is the posterior mean -- we will learn
that in class, but maybe not until Wed mar 10.