The Binomial Distribution: Mathematically Deriving the Mean and Variance @jbstatistics

Uploaded July 2013 | Updated September 2026, 2 hours ago

I derive the mean and variance of the binomial distribution. I do this in two ways. First, I assume that we know the mean and variance of the Bernoulli distribution, and that a binomial random variable is the sum of n independent Bernoulli random variables. I then take the more difficult approach, where we do not lie on this relationship and derive the mean and variance from scratch.

The Binomial Distribution: Mathematically Deriving the Mean and Variance

Proof that if events A and B are independent, so are Ac and B (and A and Bc)

Discrete Probability Distributions: The Poisson Distribution (STAT I – Full Lecture)

The Poisson Distribution: Introduction (fast version)

Finding Percentiles Using the Standard Normal Table (for tables that give the area to left of z)

Hypothesis Tests on One Mean: A t Test Example

Basics of Probability: Unions, Intersections, and Complements

The Hypergeometric Distribution: An Introduction (fast version)

Calculating Power and the Probability of a Type II Error (A One-Tailed Example)

Standardizing Normally Distributed Random Variables (fast version)

Introduction to the Negative Binomial Distribution