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Topics for Math 2030
The course had seven lectures remaining when the strike began.
It had three after the strike ended.
The following topics were covered before the strike:
Essentially, this amounts to
- Probability models and their basic properties: ie, what the basic model
is (outcomes, events), properties like additivity and inclusion/exclusion,
disjoint events, complements, etc.
- Counting and equally-likely-outcome models: permutations and combinations,
counting with and without order, sampling with and without replacement,
the multiplication rule, the binomial theorem, and how to build basic
models of simple situations (cards, dice, coins, etc.)
- Conditional probability: its definition and interpretation, the
multiplication rule and tree diagrams,
- Independent events: their definition and interpretation, and relation
to conditional probability.
- Bayes rule: Understand how to set up and use it, with both two and
- Random variables with discrete distributions: the definition of a
random variable, and calculations involving its distribution.
- Random variables with continuous distributions: densities,
distribution functions, transformations.
- Expectations: means (discrete and continuous rv), variances
(discrete and continuous rv), indicators, expectations of functions
of random variables, standard deviations, additivity of means,
scaling properties, additivity of variances for INDEPENDENT random
- Special distributions:
- Binomial: when to use it, mean and variance
- Hypergeometric: when to use it, mean
- Poisson: approximation to binomial, mean and variance
- Normal: mean and variance, use of tables, scaling
- Normal and Poisson approximations: central limit theorem and
laws of large numbers, approximations, continuity correction.
The following topics were covered after the strike:
- all of Chapter 1
- all of chapter 2 except section 2.3
- all of chapter 3 except sections 3.4, 3.6, and parts of 3.5
- sections 4.1 and 4.5
- appendix 1
This material can be found in Sections 3.1, 5.1 and 5.2.
- joint distributions (two discrete random variables):
definition, calculation of marginal distributions,
expectations, distribution of sums of rv.
- joint densities (two continuous random variables):
definition, calculation of marginal densities,
expectations, distribution of sums of rv, uniform joint
- independent random variables (discrete and continuous):
interpretation, and definitions (discrete and continuous
cases), E[XY]=E[X]E[Y] under independence, additivity of
variances under independence, sums of independent normals
(resp. Poissons) are normal (resp. Poisson).
Assignment 6 is a problem set covering this material, with some other
problems from sections 2.4, 2.5, and 3.5 (which didn't appear on an
assignment prior to the strike). You can find Assignment 6 on the
assignments page. It is not
to be handed in, but was intended to practise this material in preparation
for the final examination. An answer sheet is available, but you should try
to do the problems before looking at it.
If there had been time I would have covered parts of Chapter 6.
The topics I most regret leaving out are the geometric and exponential
distributions. If you have time, once exams are over, I recommend that
you read over sections 3.4 and 4.2 to see what was left out.