# Author Archive | Paul King

• Paul King is a full-time educator and writer based in Manhattan. He graduated Magna Cum Laude from the University of Delaware in 2009, earning his B.A. in Chemistry with Honors, as well as induction into Phi Beta Kappa. His current projects include tutoring students for the SAT, ACT, GRE, and GMAT; SAT II Subject Tests in Chemistry, Physics, and Math II, and high school AP courses including AP Statistics and AP Physics. In addition to writing for Magoosh, Paul has penned articles on AP Chemistry topics for Khan Academy. You can learn more about him at paulkingprep.com

## What is Random Walk Theory?

A random walk describes the movement of an object along some mathematical space, or the different values generated by a random variable. Random walks have applications in Finance, Economics, Chemistry, Physics, and more. In this article, we’ll introduce the idea of random walks and Random Walk Theory.

## Markov Chains

A Markov chain is a memoryless stochastic process, meaning that future states of the system depend only upon the current state. In this article, we introduce the concept of a Markov chain and examine a few real-world applications.

## Understanding Discrete Probability Distribution

A discrete probability distribution describes a random variable that can only produce distinct and finite outcomes. In this article, we explore what a discrete probability distribution looks like, and how to calculate the expected value of a random variable from the discrete probability distribution.

## What is the geometric distribution formula?

The geometric distribution formula can be used to calculate the probability of success after a given number of failures. The probabilities it generates form a geometric sequence, hence its name. Check out this article to learn more about the geometric distribution formula!

## Understanding Geometric Probability Distribution

The word “geometric” might remind you of the triangles and squares learned about back in ninth grade geometry class. However, elsewhere in mathland, “geometric” simply refers to multiplication. Thus, “geometric probability distribution” will involve the multiplication of probabilities. Let’s consider some examples.

## Stochastic Processes

A stochastic process describes the changes that a random variable takes through time. In this article, we introduce stochastic processes and some of their basic properties.

## The Basics of Probability

In this article, we focus on the basics of probability, including its definition and how to calculate it from a given sample space. We also look at basic probability rules using “and” and “or,” and practice using some example problems.

## What is conditional probability?

A conditional probability is one in which some condition has already been met. For example, if you know that it’s raining (the given condition), the probability of your baseball game getting cancelled increases. In this article, we look at conditional probability in depth.

## Continuous Probability Distribution Explained

What is a continuous probability distribution? It will be helpful to first define the terms continuous versus discrete, and then compare the two. According to Apple Dictionary, discrete means, “individually separate and distinct,” whereas continuous means, “forming an unbroken whole; without interruption.” A great way to visualize the difference is to look at a fretted […]

## Dependent Events: Definition and Examples

Two events are considered dependent if the occurrence or outcome of the first event changes the probability of the next event occurring.