MATH 3215

MATH 3215 covers basic probability, the statistical method, expectation and variance, the law of large numbers and central limit theorem, and hypothesis testing and confidence intervals.

It is a 3 credit-hour course intended for advanced undergraduates and an introduction for graduate students.

Topic List

• Combinatorics and discrete probability.
• Conditional probability, Bayes' theorem, and independence.
• Random variables.
• Hypothesis testing.
• Expectation and variance.
• Chebyshev's theorem and the law of large numbers.
• Continuous distributions.
• Joint and marginal distributions.
• Important families of distributions (Poisson, binomial, normal).
• Normal approximation and the central limit theorem.
• Parameter estimation.
• Confidence intervals.
• Chi-square and goodness of fit.

Class Structure

Lecture, homework, exam, and sometimes a project in machine learning toward the end of the semester.

Prerequisite Knowledge

Multivariable calculus.

Equivalent Courses

None

Resources

There is no textbook required by the department.

But at least two different professors have taught this while either recommending or requiring Probability and Statistical Inference by Hogg and Tannis.

Also both professors have recommended the OpenCourseware MIT class 18.05.