STAT 51600 - Basic Probability And Applications

A first course in probability intended to serve as a background for statistics and other applications. Sample spaces and axioms of probability, discrete and continuous random variables, conditional probability and Bayes’ theorem, joint and conditional probability distributions, expectations, moments and moment generating functions, law of large numbers and central limit theorem. (The probability material in Course 1 of the Society of Actuaries and the Casualty Actuarial Society is covered by this course.)

Preparation for Course
P: MA 26100 with a grade of C- or better.

Cr. 3.
Notes
Note: Prerequisites in mathematics and statistics are intended as a guide and may be satisfied through completion of equivalent or more advanced courses. Consent of the course instructor can substitute for completion of specified prerequisites, and students are invited to discuss their eligibility for enrollment with their advisors or the instructor of the course.

Student Learning Outcomes

1. Identify which discrete and continuous distributions are applicable in a given setting.
2. Use conditional probabilities, Bayes theorem, and conditional distributions.
3. Utilize joint distributions in the context of several random variables.
4. Apply the law of large numbers and the central limit theorem in asymptotic settings.
5. Derive moments and moment generating functions for discrete and continuous random variables.