Math 431: Introduction to the Theory of Probability

Student Body:

Math majors and students in the sciences and engineering

Alternatives:

Stat 309.

Subsequent Courses:

Math 632, Math 635. Students can also consider 531 for a proof based introduction to probability.

At the graduate level Math 733-734.

Course Content:

Basic Concepts:
- A mathematical model for a nondeterministic phenomenon
  - the sample space and events
  - probabilities of events
  - properties of probabilities
- Finite sample spaces, equally likely outcomes, and methods of enumeration (combinatorics)
- Conditional probability, Bayes formula, and independence
Random Variables:
- Definitions and important examples
  - the cumulative distribution function
  - expected value and variance
  - binomial random variables
  - Poisson random varaibles and approximation
  - geometric and negative binomial random variables
  - the uniform, normal, and exponential random variables
- The distribution of a function of a random variable
- Several random variables
  - definitions and examples
  - independent random variables
  - sums of independent random variables
  - conditional distributions
- Further properties of expectations
  - properties of the expected value
  - properties of variances and covariances
  - conditional expectations
The weak law of large numbers and the central limit theorem
- Markov's and Chebyshev's inequalities
- Proof of weak law of large numbers and applications
- Application of central limit theorem to parameter estimation

credits:

3. (N-A)

semester:

All

prereqs:

MATH 234 or 376 or graduate or professional standing or member of the Pre-Masters Mathematics (Visiting International) Program

UW_course_guide:

Department of Mathematics