# STATS 414: Introduction to Probability Theory

## The Pennsylvania State University

This consists of the following topics:

• What is a probability space?

• Discussion of random variables - Discrete and Continuous.

• Idea of transformations.

• Finding expectations.

• What are generating functions?

• Discussion of conditional distributions.

• The law of large numbers and convergence.

• Central limit theorems.

### Overview of the course:

This chapter covers the basics of probability theory that gives details of probability space , the differentiation of discrete and continuous random variables. Apart from these the method for finding expectations and the procedure of performing transformations of variables are also provided in this chapter. The probability and moment generating functions are also included. Details of conditional distributions , WLLN, convergence in law and probability, CLT etc. are also included.

### Prerequisites includes:

• Statistics - STAT 500 and STAT 501

• Math - Standard Calculus knowledge (MATH 140, MATH 141 and MATH 230) and linear algebra or matrix algebra (MATH 220).

Students are advised to revise their calculus lessons if they have studied a few years ago.

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