#### 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