Foundations of Probability and Random Variables

Johns Hopkins University via Coursera

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Overview

The course "Foundations of Probability and Random Variables" introduces fundamental concepts in probability and random variables, essential for understanding computational methods in computer science and data science. Through five comprehensive modules, learners will explore combinatorial analysis, probability, conditional probability, and both discrete and continuous random variables. By mastering these topics, students will gain the ability to solve complex problems involving uncertainty, design probabilistic models, and apply these concepts in fields like machine learning, AI, and algorithm design. What makes this...

Syllabus

Course Introduction

This course provides a comprehensive introduction to fundamental concepts in probability and statistics, focusing on counting principles, permutations, combinations, and multinomial coefficients. You will explore probability axioms, conditional probabilities, and Bayess Formula while using Venn diagrams to visualize events. The course covers random variables, including discrete and continuous types, expected values, and various probability distributions. Practical applications in R programming and data analysis tools will enhance understanding through simulations and real-world problem-solving. By the end, you will be equipped to analyze and interpret statistical data effectively.

Combinatorial Analysis

This module covers the usefulness of an effective method for counting the number of ways that things can occur. Many problems in probability theory can be solved simply by counting the number of different ways that a certain event can occur.

Probability

This module introduces the concept of the probability of an event and then shows how probabilities can be computed in certain situations.

Conditional Probability and Independence

This module explores one of the most important concepts in probability theory, that of conditional probability. The importance of this concept is twofold. First, you will be interested in calculating probabilities when some partial information concerning the result of an experiment is available; in such a situation, the desired probabilities are conditional. Second, even when no partial information is available, conditional probabilities can often be used to compute the desired probabilities more easily.

Discrete Random Variables

This module discusses the function of outcomes rather than the actual outcomes themselves. In particular, you will examine random variables that can take on at most a countable number of possible values. You can call these types of variables, discrete random variables.

Continuous Random Variables

This module extends the concept of random variables where the outcomes cannot be counted. You will explore probability density functions, cumulative distribution functions, the normal distribution and other common distributions.