Here you can find what has been done in the lectures, and from time to time also what is planned for upcoming lectures.
Final exam (McDonnell, room 162) Chapters 1 through 8 (excluding material not covered in class or by self-study).
Exam review (Cupples 1, room 115) Review of the course.
Section 8.3 Central limit theorem.
Section 7.5 Conditional expectation. Conditional variance.
Section 8.2, 7.4, 7.5 The weak law of large numbers. Correlation. Conditional expectation.
Section 7.4 Covariance. Variance of sums.
Thanksgiving No class.
Thanksgiving No class.
Section 7.2, 7.4 Expectation of a sum of random variables.
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.
In-class exam Chapters 4, 5, 6.1 - 6.3, and section 8.2.
Exam review Examples from chapters 4, 5, and 6.
Section 6.2, 6.3 Independent random variables. Sums of independent random variables.
Section 6.1 Joint distribution functions. Joint probability mass functions. Joint density functions.
Section 5.7, 6.1 Functions of a random variable. Joint distribution functions.
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.
Section 5.4 Normal random variables.
Section 5.2, 5.3 More properties of expectation of continuous random variables. Uniform random variables.
Section 5.2, 8.2 Expectation and variance of continuous random variables. Markov's inequality. Chebyshev's inequality.
Section 4.9, 5.1 Properties of the cumulative distribution function. Continuous random variables.
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.
Section 4.6 Expectation and variance of binomial random variables.
Section 4.5, 4.6 Variance of a random variable. Bernoulli random variable. Binomial random variable.
Section 4.3, 4.4 St. Petersburg Lottery (see also Problem 4.30). The Two Envelope Paradox (see also Self-test problem 4.7).
Fall Break No class.
Section 4.3, 4.4 Expected value of a random variable.
Section 4.2 Discrete random variables. Probability mass function.
Section 4.1 Random variables. Cumulative distribution function.
In-class exam Covering the material in the first three chapters of the book.
Exam review Review continued, and discussion of Practice Exam.
Exam review Review of the first three chapters.
Section 3.5 Conditional probability is a probability.
Section 3.4 The probabilistic method. The Monty Hall problem.
Section 3.4 Problem 2.T.9 from homework. Independence of several events.
Section 3.3, 3.4 Bayes' formula. Odds. Definition of independent events.
Section 3.3 The Norwegian King's sisters. Bayes' formula.
Section 3.2 Conditional probabilities.
Section 2.5, 2.7 The Birthday Paradox. Probability as a measure of belief.
Section 2.4, 2.5 The general inclusion-exclusion identity. Sample spaces with equally likely outcomes.
Section 2.4 Some simple propositions regarding probability.
Section 2.2, 2.3 DeMorgan's laws. Axioms of probability.
Section 2.2 Sample space, events, union/intersection/complement of events.
Section 1.5, 1.6 Multinomial theorem. Dividing indistinguishable objects into groups.
Section 1.4, 1.5 Binomial and multinomial coefficients.
Labor Day No class.
Section 1.3, 1.4 Permutations and combinations.
Section 1.1, 1.2 Introduction to the course. Basic counting.