Free online courseProbability and Distributions Crash Course

Course Description

Probability and Distributions Crash Course is a free online course in Basic Education, within Statistics, designed to build strong intuition and practical skill in probabilistic thinking. It starts from foundational ideas such as sample spaces, events, and counting methods, then quickly moves into core tools used to reason under uncertainty in real situations.

You will develop confidence with conditional probability, independence, the law of total probability, and Bayes’ theorem through clear explanations and applied examples, including quality control and testing scenarios. Along the way, you’ll see how combinatorics connects to probability calculations and how common pitfalls are avoided by setting up problems correctly.

The course then introduces random variables and probability distributions, covering essential discrete and continuous models such as Bernoulli, binomial, multinomial, normal, Poisson, geometric, exponential, gamma, and chi-squared distributions. You will learn how to compute probabilities, work with transformations and rescaling, and interpret parameters in ways that match real data-generating processes.

To round out the toolkit, the course develops expectation, variance, standard deviation, covariance, and correlation, with worked examples that show how these quantities are computed and why they matter. It also covers foundational results and bounds including Markov’s inequality, Chebyshev’s inequality, the law of large numbers, and the central limit theorem, connecting theory to intuition and approximations used in practice. Moment generating functions and measure-based perspectives are introduced to deepen understanding and support more advanced study.