Math 493 - Probability

Lectures

Here you can find what has been done in the lectures, and from time to time also what is planned for upcoming lectures.

Tuesday December 16th.

Final exam (McDonnell, room 162) Chapters 1 through 8 (excluding material not covered in class or by self-study).

Thursday December 11th.

Exam review (Cupples 1, room 115) Review of the course.

Monday December 8th.

Section 8.3 Central limit theorem.

Friday December 5th.

Section 7.5 Conditional expectation. Conditional variance.

Wednesday December 3rd.

Section 8.2, 7.4, 7.5 The weak law of large numbers. Correlation. Conditional expectation.

Monday December 1st.

Section 7.4 Covariance. Variance of sums.

Friday November 28th.

Thanksgiving No class.

Wednesday November 26th.

Thanksgiving No class.

Monday November 24th.

Section 7.2, 7.4 Expectation of a sum of random variables.

Friday November 21st.

Section 6.3, 7.2 Sums of independent normal, Poisson and binomial random variables. Expectation of a sum of random variables.

Section 6.4, 6.5 Self-study. Conditional distributions. Discrete and continuous cases.

Wednesday November 19th.

In-class exam Chapters 4, 5, 6.1 - 6.3, and section 8.2.

Monday November 17th.

Exam review Examples from chapters 4, 5, and 6.

Friday November 14th.

Section 6.2, 6.3 Independent random variables. Sums of independent random variables.

Wednesday November 12th.

Section 6.1 Joint distribution functions. Joint probability mass functions. Joint density functions.

Monday November 10th.

Section 5.7, 6.1 Functions of a random variable. Joint distribution functions.

Friday November 7th.

Section 5.4, 5.5 Normal approximation to the binomial distribution. Exponential random variables.

Section 5.6 Self-study. The gamma distribution. The Weibull distribution. The Cauchy distribution. The beta distribution.

Wednesday November 5th.

Section 5.4 Normal random variables.

Monday November 3rd.

Section 5.2, 5.3 More properties of expectation of continuous random variables. Uniform random variables.

Friday October 31st.

Section 5.2, 8.2 Expectation and variance of continuous random variables. Markov's inequality. Chebyshev's inequality.

Wednesday October 29th.

Section 4.9, 5.1 Properties of the cumulative distribution function. Continuous random variables.

Monday October 27th.

Section 4.7 The Poisson random variable as an approximation of the binomial random variable. Expectation and variance of binomial random variables.

Example 7d is self-study. This is a comprehensive example that touches on most of the concepts we have seen in the course so far.

Section 4.8 Self-study. The geometric random variable. The negative binomial random variable. The hypergeometric random variable.

Friday October 24th.

Section 4.6 Expectation and variance of binomial random variables.

Wednesday October 22nd.

Section 4.5, 4.6 Variance of a random variable. Bernoulli random variable. Binomial random variable.

Monday October 20th.

Section 4.3, 4.4 St. Petersburg Lottery (see also Problem 4.30). The Two Envelope Paradox (see also Self-test problem 4.7).

Friday October 17th.

Fall Break No class.

Wednesday October 15th.

Section 4.3, 4.4 Expected value of a random variable.

Monday October 13th.

Section 4.2 Discrete random variables. Probability mass function.

Friday October 10th.

Section 4.1 Random variables. Cumulative distribution function.

Wednesday October 8th.

In-class exam Covering the material in the first three chapters of the book.

Monday October 6th.

Exam review Review continued, and discussion of Practice Exam.

Friday October 3rd.

Exam review Review of the first three chapters.

Wednesday October 1st.

Section 3.5 Conditional probability is a probability.

Monday September 29th.

Section 3.4 The probabilistic method. The Monty Hall problem.

Friday September 26th.

Section 3.4 Problem 2.T.9 from homework. Independence of several events.

Wednesday September 24th.

Section 3.3, 3.4 Bayes' formula. Odds. Definition of independent events.

Monday September 22nd.

Section 3.3 The Norwegian King's sisters. Bayes' formula.

Friday September 19th.

Section 3.2 Conditional probabilities.

Wednesday September 17th.

Section 2.5, 2.7 The Birthday Paradox. Probability as a measure of belief.

Monday September 15th.

Section 2.4, 2.5 The general inclusion-exclusion identity. Sample spaces with equally likely outcomes.

Friday September 12th.

Section 2.4 Some simple propositions regarding probability.

Wednesday September 10th.

Section 2.2, 2.3 DeMorgan's laws. Axioms of probability.

Monday September 8th.

Section 2.2 Sample space, events, union/intersection/complement of events.

Friday September 5th.

Section 1.5, 1.6 Multinomial theorem. Dividing indistinguishable objects into groups.

Wednesday September 3rd.

Section 1.4, 1.5 Binomial and multinomial coefficients.

Monday September 1st.

Labor Day No class.

Friday August 29th.

Section 1.3, 1.4 Permutations and combinations.

Wednesday August 27th.

Section 1.1, 1.2 Introduction to the course. Basic counting.