Back to Tom Salisbury's Home Page
MATH 2030 3.0AF (Fall 2007)
Elementary Probability
Announcements and documents will be posted here as they
become available.
Documents
Announcements
- Final grades have been submitted, and are also posted outside my
office door. The exam grades were a bit low, so the final scores have
been adjusted upwards a bit. Grades were consistent between the sections.
(In other words, since our section did very slightly better on the exam,
and therefore has a slightly higher average).
- People are welcome to come to my office and look over their exams.
There are also solutions that people can look at in my office.
Unfortunately you cannot take either the exam or solutions away.
- Access to the assignment solution pages has been withdrawn. If you
took this course and now need access to those pages, feel free to contact
me.
Topics
While we followed the text, we did not
necessarily cover all topics, nor did we necessarily cover the topics in
the order the textbook presents them.
With this in mind,
the basic list of topics we covered, in the order we treated them, is
as follows:
- The model for probabilities, random variables, and events
(Sections 1.1 - 1.3)
- Counting (appendix 1)
- Independence and Conditional Probability (Sections 1.4 and 1.6)
- Bayes rule (Section 1.5)
- Representing discrete and continuous distributions (parts of
Sections 3.1 and 4.1)
- Cumulative Distribution functions, their relation with densities
and discrete distributions, and using them to compute distributions
of transformed random variables (parts of Section 4.5)
- Binomial and Normal distributions (Section 2.1 and 2.2),
and normal approximations to the binomial distribution (Section 2.2)
- Expectations for discrete and continuous random variables (parts of
Section 3.2 and 4.1), including the method of indicators.
- Variances (part of Section 3.3), along with calculation of means and
variances for distributions like the Binomial and Normal.
- Independence of random variables, and its consequences for expectations
and variances.
- The hypergeometric distribution (Sections 2.5 and 3.6)
- The law of large numbers, Chebyshev's inequality, and the Central Limit Theorem (Section 3.3)
- Normal approximations to more general
sums of independent random variables (Section 3.3).
- The poisson distribution and poisson approximation (Sections 2.4 and 3.5)
- The geometric (and negative binomial) distribution (Section 3.4)
- The exponential (and gamma) distribution (Section 4.2)
- Joint and marginal densities (Sections 5.1 and 5.2)
If we had had more time we would have looked at: moment generating functions, covariance, and
conditional densities.
We did not cover Sections 2.3, 4.3, 4.4, or 4.6.