Department:
Statistics >
Course:
Prob Theory & Math Stat 1
STAT
641

## Prob Theory & Math Stat 1

### Hours

3.0 Credit, 3 Lecture, 0 Lab

### Semester

Fall
Axioms of probability; combinatorics; random variables, densities and distributions; expectation; independence; joint distributions; conditional probability; inequalities; derived random variables; generating functions; limit theorems; convergence results.

## STAT 641

Upon successful completion of the course, the student will be able to:

## Apply Fundamentals

Apply fundamentals of set theory and basic set operations

## Enumerate the Elements

Enumerate the elements of a discrete sample space

## Solve Problems

Solve problems using axioms of probability, conditional probability, independence, and Bayes theorem

## Describe the Properties

Describe the properties of the named distributions

## Manipulate the PDF and CDF

Manipulate the pdf and cdf of univariate and multivariate discrete and continuous random variables to calculate probabilities and find joint and conditional distributions

## Find Moments

Find moments and moment generalized functions

## Derive Distributions

Derive distributions for transformed random variables and order statistics

## Use Inequalities

Use inequalities to create bounds on probabilities and expected values

## Verify Convergence

Verify convergence in probabilty, distribution, and mean square

## Prove the Central Limit Theorem

Prove the Central Limit Theorem (iid and non-identical finite variance versions) and demonstrate it by simulation