Fall 2008
STAT 7010 – Mathematical Statistics I
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Date |
Section |
Assignment |
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Aug 21 |
Introduction
to probability: sample spaces; definition of probability; computing probability
of events. Combinatorics.
(Sections 2.2, 2.3, 2.6, 2.7). |
Read
Chapter 1, it is beautiful! Read
Chapter 2 sections 2.1-2.3; 2.6-2.7 Hw#1: ex. 2.2.1, 2.2.10, 2.2.18,
2.2.26, 2.2.31, 2.3.2, 2.6.17, 2.6.53, 2.7.10, 2.7.14, 2.7.22 text. Problem 8 on hand-out (from the ones on
the SOA* exam. It is on page 7 of 82); pb. 2.1.10 (A plausible paradox in
chances), 2.2.7 from Ruma Falk hand-out.
Hw#1 is due Aug 28. Suggested
problems: 2.2.32, 2.2.40, 2.6.18, 2.7.10, 2.7.20, 2.7.23 text. Have a
look at: 2.2.2, 2.2.6, 2.2.7, 2.2.8, on the hand-out from Ruma Falk book. SOA=Society
of Actuaries |
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Aug 28 |
Conditional
probability, independence. Bayes’ Theorem. |
Read sections
2.4, 2.5. Read defining independence for more than 2 events (page 75). Read
the notes on Applications of counting. Hw#2: ex:2.4.46, 2.4.48, 2.5.2,
2.5.7, 2.5.22, 2.5.29; problems 53, 56 from handout. Also, see additional problems. Suggested
problems: as many as you want from 2.4, 2.5 and handout. |
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Sept 4 |
Discrete
random variables. The hypergeometric and binomial models. |
Hw#3 see TI commands for
statistical applications. Minitab
commands for computing binomial probabilities and beyond. |
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Sept 11 |
Discrete
Random Variables. The Geometric and Poisson distributions. Expected values,
variance. |
Read: section 3.3, 3.5 (pay attention to Corollary to
Theorem 3.5.3 page 187: see how it applies to pb. 3.5.27), 3.6 (see important result Theorem 3.6.2), 4.2 (pay attention to the Case studies 4.2.2 an 4.2.3), Hw#4 due Sept. 18: 3.3.7, 3.5.2, 3.5.7, 3.6.3,
4.2.11, 4.2.11, 4.2.15, 4.2.17, 4.2.19 and problems: 31, 48, 52 from
hand-out. Suggested problems: 3.3.1, 3.5.3, 3.5.15, 3.5.16,
3.5.27, 4.2.17, 4.2.21. |
|
Sept 18 |
More
examples on discrete distributions. The geometric distribution: the
memoryless property. Continuous distributions: the exponential distribution. |
Read: 3.4 pages 161-171; 3.5 Expected
values: the definition for the expected value of a continuous random variable
is similar to the one for the discrete case, only that the integral replaces
the sum. (see page 175) Back to 4.2: read on page 289: intervals between events:
the Poisson/Exponential relationship Formula sheet: “A list
of needful things” Hw#5 due Sept 25: 3.4.1, 3.4.7, 3.5.9, 3.5.14,
problem 55 on the Society of Actuaries handout, and see additional problems document. |
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Sept 25 |
Expected
values. The relationship between the Poisson and the exponential
distribution. The normal distribution. See
link to Resources on main page. You will see a practice
test there with solutions and some links to some notes (most of them are from
2006 but some of them contain examples in Minitab and Maple) |
Read: 3.5; 4.2 -4.3(page 289-295) Hw#6 due Oct. 2: 4.2.26, 4.2.29, 4.3.1.(do not
use the table, use the TI83 or Minitab; notice that the integral represents a
probability!); 4.3.2(a, b), 4.3.6, 4.3.7, and problems 1, 8 and 10 on the document. |
|
Oct 2 |
Joint
densities: the discrete case.(3.7) Expected
value and variance of linear combinations of random variables (3.9) |
Read: 3.7: pp203-205; Read Example 3.7.12 and Random
samples on page 218. 3.9: pp226-236 (you may skip the continuous examples); Suggested practice problems (remember you can see the
solutions to all problems in chapter 3 in Hw#7 due Oct. 9: Work the problems in the
attached document. Look later in |
|
Oct 9 |
The
Central Limit Theorem. The normal approximation to the binomial distribution. |
Read
4.3. No
Homework given. Midterm take home. |
|
Oct 16 |
The
Moment Generating Function. Properties of sums of independent Binomial random
variables and Poisson random variables. Linear
combinations of normal independent random variables. |
Read section 3.12. Read also Using Moment-Generating
Functions to find moments and variances (page 261-265). Revisit the normal distribution: 4.3 pages 307-314. Practice on pb: 3.12.2, 3.12.3, 3.12.4, 3.12.5, 3.12.18,
3.12.19, 3.12.20, 3.12.21 3.12.23, 3.12.24. Most of the problems were done in
class, and remember the solutions are available in Hw#8 due Oct 23: 4.3.17, 4.3.18, 4.3.19, 4.3.22,
4.3.33, 4.3.34, and the problems in the attached document. |
|
Oct 23 |
Transformations
of distributions. The |
Read: Transformations
(page 158 text and the examples that follow); transformations continuous case
(page 171). Read: 4.4 (the geometric
distribution), 4.5 (the Negative Binomial distribution); 4.6 (The Gamma
distribution). Hw#9 due Oct 30: from handout given in class:
page 189 pb. 11, 12, 13, 14; chapter 4: 4.5.2, 4.6.1, 4.6.3, 4.6.4. More to
come. |
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Oct 30 |
Chapter 5: Maximum Likelihood Estimators and the Method
of Moments |
Read: Section 5.2 text. Hw#10 due Nov 6: 5.2.6, 5.2.7, 5.2.9, 5.2.15,
5.2.17 (notice that we did in class the MLE of the Poisson distribution). |
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Nov 7 |
Chapter 5: Interval estimation. Properties of Estimators
(5.3 and 5.4) |
Read Sections 5.3- 5.4 text. Hw#11 due Nov 13 (last hw assignment, rejoice!):
from handout (Rice) page 241: EX. 5, 7, 16, 17, 18, MORE TO COME |
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Nov 13 |
Project
presentations. Take-home midterm will be given. |
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Nov 20 |
Project
presentations. Take-home midterm due. |
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Nov 27 |
No class.
Thanksgiving holiday. |
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Dec 4 |
Final exam. |
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