References: Random variables and expected value

Source material

Source curriculum (structural mirror, cited as further study):
• Khan Academy, "Random variables" (Statistics & Probability)
  Author: Sal Khan and the Khan Academy team
  Unit page: https://www.khanacademy.org/math/statistics-probability/random-variables-stats-library
  License: CC BY-NC-SA 4.0
Clawdemy's lessons are original prose that follows the pedagogical arc of this
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Source-scope note: this lesson mirrors Khan's "Random variables" unit
(discrete random variables, expected value, variance) and restates it in
Clawdemy's voice with original examples (the die, the two bets, the coin
wager). The machine-learning framing (a loss as an expected error, a reward as
an expected payoff, performance as an expectation) is Clawdemy framing.
Continuous random variables are introduced in the next lesson, on the normal
distribution. Exact per-unit URLs are verified at promotion.

Read this next

• Khan Academy: Random variables by Sal Khan and the Khan Academy team. The full unit this lesson mirrors, with videos and practice on probability distributions, expected value, and the variance of a random variable, free and CC-licensed. The place to drill expected-value calculations until they are quick.

Going deeper

A short, durable list. Both are free.

• Khan Academy, “Summarizing quantitative data” (within the course above). Revisit the mean and variance of a dataset; expected value and the variance of a random variable are the same ideas applied to a distribution rather than a list of numbers.
• Khan Academy, “Modeling data distributions” (within the course above). The bridge to the next lesson: once values fill a continuous range, the normal distribution becomes the workhorse, and expected value and standard deviation carry straight over.

Adjacent topics

Where this sits inside this track.

• Updating beliefs with evidence: Bayes’ theorem. The previous lesson, which closed Phase 2. The track shifts from single events to numbers and whole distributions.
• The bell curve: the normal distribution. The next lesson. It takes the expected value and standard deviation from here into the continuous setting, with the empirical rule and z-scores.
• Summarizing data: center and spread. Phase 1. Expected value and variance of a random variable are the distribution-level versions of the mean and variance you computed for data there.