Unit 3 of 15
Probability and Statistical Reasoning
- 4 lessons
- Videos 15 to 18
Predictions are made under uncertainty. This unit teaches the probability and statistics the course uses, from conditional probability and distributions to expectation and sampling uncertainty.
Conditional probability keeps track of the reference group, and Bayes' rule combines a base rate with new evidence. Random variables are described by probability mass functions, densities and cumulative distribution functions, with binomial and normal models as examples. Sums and integrals are introduced where they are needed. Expectation, variance, covariance and conditional expectation summarize a distribution and connect it to predictions. The unit ends with estimators, standard errors and confidence intervals, and with the assumption of independent and identically distributed observations.
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.
Conditional Probability and Distributions
Conditional Probability and Bayes' Rule
How conditional probability fixes a reference group, how Bayes' rule combines a base rate with evidence into a posterior probability, and how independence differs from conditional independence.
Video 15
Random Variables and Probability Distributions
How a random variable turns outcomes into numbers, how a probability mass function, a density and a cumulative distribution function give probabilities, and how binomial and normal models are built.
Video 16
Expectation and Sampling Uncertainty
Expectation, Variance, and Covariance
How expected value, variance, covariance and correlation summarize a probability model, how a covariance matrix collects them, and how a conditional expectation gives the best prediction under squared error.
Video 17
Sampling, Estimation, and Statistical Uncertainty
How an estimator varies through its sampling distribution, how independent and identically distributed data give the standard error, what the law of large numbers and confidence intervals promise, and how selection bias misleads.
Video 18