Department of Mathematics

Van Vleck Hall, 480 Lincoln Drive, Madison, WI

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.

UW-Madison Department of Mathematics
Van Vleck Hall
480 Lincoln Drive
Madison, Wi  53706

(608) 263-3054

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