Probability

The rules of chance: events, conditioning, independence, and random variables.

In suggested reading order:

1. Introduction to Probability. The basic language of probability, namely experiments, sample spaces, events, and the three axioms every probability must obey.
2. Conditional Probability. The probability of an event once we know that another event has occurred.
3. Statistical Independence. Two events are independent when knowing that one happened does not change the probability of the other.
4. Bayes' Theorem. A rule for reversing a conditional probability, turning P(evidence | hypothesis) into P(hypothesis | evidence).
5. Random Variables. A random variable assigns a number to each outcome of a random experiment; its distribution is described by a PMF, a PDF, or a CDF.
6. Expected Value. The probability-weighted average of a random variable's values, interpreted as its long-run average and as the balance point of its distribution.
7. Variance of a Random Variable. The expected squared distance of a random variable from its mean, measuring how spread out its distribution is.