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
- A mathematical model for a nondeterministic phenomenon
- 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
- Definitions and important examples
- 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