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MATH 2030 3.00MW (Winter 2011)
Announcements and documents will be posted here as they
- Parts of the exam were quite well done, and parts were not. I think
it was a fair exam, with some routine problems and some difficult problems.
Pains were taken to make the grading fair. The exam grades were a bit on the low
side, but not dramatically so. People who
want to look over their exams are welcome to do so - just make an appointment
with me over the summer.
Here is a stem and leaf plot of the
- Given the concerns that were raised about the grading of the 2nd midterm,
and the slightly low scores on the final, I was fairly generous about how I
Here is a stem and leaf plot of the
out of 100, and reflecting all the adjustments I made to the
- The course meets MWF 8:30-9:20 in CB121.
- The textbook is Probability by Pitman. The bookstore has copies.
Documents and links
One of my projects this term is to digitize my course notes. I don't promise to keep these up-to-date, nor to include every lecture in the notes. But what I do manage to complete I will mount here. I have linked to the lecture notes as part of the topics list below.
Regarding the final exam: you are responsible for the material covered in
class and on the assignments. This is roughly Chapters 1-4 of the text, plus
Appendix 1 and
a little bit from Section 6.4; Here is a list of exceptions,
ie topics from the text that we didn't cover, or which you're not responsible for:
If you are looking at old exams, note that some years, students were
responsible for the gamma and negative binomial distributions (you're not).
In past years correlation wasn't covered. In some past years, joint and marginal densities were also covered. Now that is only dealt with in MATH 2131, so you
are only responsible for discrete joint and marginal distributions.
- Empirical distributions (in 1.3)
- Odds rations (in 2.3)
- Skew normal approximations (in 2.2 and 3.5)
- The negative binomial distribution (in 3.4)
- The gamma distribution (in 4.2)
- Hazard rates (in 4.3)
- Order statistics (in 4.6)
You should be reading ahead in the textbook, to be prepared to ask about
topics that are unclear, when they come up in class. Be aware that though
we will follow the text, we will not
necessarily cover all topics, nor will we necessarily cover the topics in
the order the textbook presents them.
With this in mind, here is
the basic list of topics we will cover, in the order we will treat them.
You can tell which days each was covered by checking out the on-line course notes.
- The model for probabilities, random variables, and events
(Sections 1.1 - 1.3) [omit: empirical distributions]
- Counting (appendix 1)
- Independence and Conditional Probability (Sections 1.4 and 1.6)
- Bayes rule (Section 1.5)
Part III (corrected)
- Representing discrete and continuous distributions (Sections 3.1 [pp. 140-141] and 4.1 [pp. 259-271])
- Cumulative Distribution functions, their relation with densities
and discrete distributions (Section 4.5)
- Using cdf's to compute distributions
of transformed random variables (Section 4.5, pp. 320-323)
- Part IV (corrected)
- Binomial and Normal distributions (Sections 2.1 and 2.2),
- Normal approximations to the binomial distribution (Section 2.2) [omit: skew normal approximation]
- Expectations for discrete and continuous random variables (Section 3.2, and pp. 273-275 of Section 4.1), including the method of indicators.
- Variances (pp. 185-189 of Section 3.3), along with calculation of means and variances for distributions like the Binomial and Normal.
- The hypergeometric distribution (Sections 2.5 and 3.6)
- Part V (version v)
- Independence of random variables (p. 151 of Section 3.1), and its consequences for expectations and variances (p. 193 of Section 3.3).
- The law of large numbers, Chebyshev's inequality, and the Central Limit Theorem (pp. 191-197 of Section 3.3)
- Normal approximations to more general
sums of independent random variables (p. 196 of Section 3.3).
- The Poisson distribution and Poisson approximation (Sections 2.4 and 3.5)
- The geometric distribution (Section 3.4)
- The exponential distribution and relation to the Poisson (Section 4.2)
- The negative binomial and gamma distributions (Sections 3.4 and 4.2: were mentioned, but you're not responsible for them.)
- Joint and marginal distributions, correlation and covariance (for discrete r.v. only) (Sections 3.1 and 6.4)