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

Apply fundamentals of set theory and basic set operations

Enumerate the elements of a discrete sample space

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

Describe the properties of the named distributions

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 and moment generalized functions

Derive distributions for transformed random variables and order statistics

Use inequalities to create bounds on probabilities and expected values

Verify convergence in probabilty, distribution, and mean square

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