Expectation and Variance from High School to Grad School

Many people find the ideas of Expectation and Variance confusing. In part this is because the way we view these concepts changes as our understanding grows in sophistication. In this post we'll look at the way these definitions change from their basic High School intro to the view of Rigorous Probability Theory.

Working with Probability Distributions

Learn about Discrete and Continuous probability distributions as well as the types of questions that they can both answers. This post also discusses the relationship between the Binomial and Beta distributions.

Monte Carlo Simulations in R

Monte Carlo simulations are very fun to write and can be incredibly useful for solving ticky math problems. In this post we explore how to write six very useful Monte Carlo simulations in R to get you thinking about how to use them on your own.

Han Solo and Bayesian Priors

There is an iconic probability problem in The Empire Strikes Back! Han Solo is told that navigating an asteroid field is extremely unlikely to be successful. However not only does he navigate the asteroid field successfully, but we know he will. Learn how we can use Bayesian Priors to reconcile C3POs frequentist views on probability with our natural reasoning.

One in a Million and e

Euler's number (the mathematical constant e) shows up in a variety of unexpected places. One of them is in Probability. A common way of expressing probabilities is to say "there's a 1 in a million chance!". In this post we find out how that way of viewing probabilities eventually leads us to Euler's number.

Understanding Variance, Covariance, and Correlation

An explanation of Variance, Covariance and Correlation in rigorous yet clear terms providing a more general and intuitive look at these essential concepts.