Unit 6 of 13
Discrete Probability Distributions
- 7 lessons
- Videos 37 to 43
Standard discrete distributions describe simple random mechanisms. This unit covers the discrete uniform, Bernoulli, binomial, geometric, negative binomial, hypergeometric and Poisson distributions.
Each distribution is linked to the experiment it models, with its support, probability formula, mean and variance. The binomial counts successes in a fixed number of independent trials with a common success probability, the geometric and negative binomial count the trials needed for the first or a later success, and the hypergeometric counts marked items in a sample drawn without replacement. The Poisson distribution models a count over an exposure, with parameter rate times exposure under a constant-rate model, and approximates the binomial when trials are many and successes rare.
Every lesson will be one video. The videos are coming soon, and each lesson page already has the definitions and an example for every key term.
Uniform and Bernoulli Distributions
The Discrete Uniform Distribution
How a discrete uniform distribution puts equal mass on a finite set of values, how to count support values and events, and how symmetry and the sum-of-squares identity give the mean and variance of consecutive integers.
Video 37
The Bernoulli Distribution
How a Bernoulli variable records one success or failure as 1 or 0, what its parameter means, why its mean is the success probability, and when its variance is zero or as large as it can be.
Video 38
Counting and Waiting in Independent Trials
The Binomial Distribution
How the binomial distribution counts successes in a fixed number of independent trials with a common success probability, where its probability formula comes from, its mean and variance, and how to find tail probabilities.
Video 39
The Geometric Distribution
How the geometric distribution counts trials up to the first success, how the trial-count and failure-count conventions differ, and how geometric series give its tail, memoryless property, mean and variance.
Video 40
The Negative Binomial Distribution
How the negative binomial distribution counts the trials needed for the rth success, why its stopping rule fixes the last trial, and how the failure-count form, geometric waiting times and binomial tails describe it.
Video 41
Finite Populations and Poisson Counts
Hypergeometric Distributions
How the hypergeometric distribution counts marked items in a uniform sample drawn without replacement from a finite population, with its support, its dependent draws and the finite population correction to its variance.
Video 42
Poisson Distributions
How the Poisson distribution models a count over a fixed exposure, when its parameter is rate times exposure, how the exponential series normalizes it, why its mean and variance are equal, and when it approximates a binomial.
Video 43