Introduction to Probability and Statistics

Course Overview

This is a 400-level theoretical-practical mathematical course in Probability. For your reference, the Calculus I and Calculus II courses are 100-level while Calculus III is a 200-level course. The objective is to know the fundamental tools of probability that are needed to understand statistics. Some topics that need to be mastered are Probability spaces, properties of probability, probability distributions, expectation, elementary limit theorems and conditional expectation and statistical hypothesis testing.

Brief Course Description: The course will be divided mainly in three parts:

• Theoretical framework of probability: Become familiar with basic concepts in probability, such as probability spaces, sample spaces, probability functions, etc. It is important to understand conditional probability and independence as they are the foundation of modern probability and statistics.
• Random Variables: Understand what is a random variable and how it becomes one of the central objects in the usage of probability in real life. Also it will be important to understand how random variables arise from probability spaces and understand the most common distributions of random variables and its statistics as expectation and variance. Finally, we will cover a central topic in modern theory of probability: Conditional Expectation.
• Applications of Probability and the usage of R: Learn how to use R as a tool to help us visualize and understand the most important concepts in probability.

Prerequisites

• MTH 243

Textbooks

• Probability and Mathematical Statistics: Theory, Applications, and Practice in R by Mary C. Meyer. SIAM.

Grading

• Exam 1: 20%
• Exam 2: 20%
• Homework: 30%
• Cumulative Final Exam: 30%

Important Note: A requisite to pass the class is to score 60% or more in any or the 3 exams. That is, you need to pass at least one exam to pass the class. If you fail all 3 exams but you have a passing average, you will still fail the class.