Suggestions for Quiz & Test
preparation
Quiz I Friday, 24 January
Study: examples of sample spaces, events, axioms of a probability measure,
simple examples of probability spaces (die, coin flips, etc.), equiprobable
sample spaces (aka discrete uniform law), how to prove two sets are equal,
de Morgan’s laws, inclusion-exclusion principle for two or three sets,
Romeo-Juliet example of a continuous probability model. Also, review HW
1 solutions.
Quiz II Friday, 31 January
Study: definition of conditional probability, examples of conditional
probability, examples of partitions of a sample space, multiplication rule,
total probability theorem, Bayes’ theorem, definition of independence of two
events. Read carefully sections 1.3, 1.4 and the beginning of 1.5. Review
HW 2 solutions.
Quiz III Friday, 21 February
Study: pmf of a random variable, expected value, variance. This material is
included in sections 2.1 through 2.4.
Test II Wednesday, 12 March
Study Chapter 2, Discrete Random Variables
The test will include pmf, joint pmf, conditional pmf, functions of r.v.,
expectation, mean, variance, linearity of expectation, independent r.v.,
properties of variance, conditional mean and variance.
The focus will be upon Bernoulli, binomial, geometric and uniform r.v.
(You will be given mean, variance.) You will not be tested upon
conditional independence.
Review the derivation of expectation and variance of the binomial r.v.
using a sum of Bernoulli r.v.
Part I will consist of several very short questions.
Part II will consist of four questions. You may select any three of the
four.
Hints: Study textbook problems 3, 4a, 7, 13, 16ab, 19a, 20, 23a, 26a, 31,
38, 39, 40*, 41a
Also MIT Quiz 1, Fall 2009, problems 1(f, g, h, i, j), 2e, 3 and MIT Quiz
1, Fall 2010, problem 1 (parts 1, 2, 5 only)
Quiz IV Friday, 28 March
Study: joint pdfs, cdf technique for finding pdf of g(X).
marginal pdf, conditional pdf, Gaussian and standard normal
distribution.
Review problem 1 of MIT problem set 6, and problems 13, 15 (chapter
3, Bertsekas) and problems 1 – 4 (chapter 4).
Review Buffon needle problem and stick-breaking problem.
Quiz V Friday, 4 April
Study: moment generating functions; review joint pdfs, conditional pdfs.
Review sections 3.4, 3.5 and study 4.4.
Gambling is part of the human condition. I love it. I have the best time
gambling. I've been winning fortunes, and I've been losing them.
- Jerry Lewis
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