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probability

Linearity of expectation

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Taught in

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Required by

Local knowledge map

Local knowledge map

Chebyshev's inequality Correlation Population versus sample Standard error Sums of independent random variables The binomial distribution The sampling distribution of a mean Covariance Mean under a linear transformation Sums of independent variables The Gaussian-noise / squared-loss connection The indicator trick The sample average as a random variable Linearity of expectation A statistic is a random variable, revisited Conditional expectation Conditional probability Discrete versus continuous: a first look Expectation for a continuous variable Expected value of a function of X (LOTUS) Expected value: the long-run average interpretation Functions of a random variable Gambler's ruin Games of chance and expected winnings Indicator random variables Joint probability mass functions Linear transformations, Y=aX+b Mean squared error Probability vocabulary for ML: Bayes' theorem,… Surprise and entropy The Bernoulli distribution The Poisson distribution The discrete uniform distribution The probability mass function Two random variables at once Variance under scaling Variance, defined Expected value Random variables Counting permutations combinations Counting-based probability

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Solid arrows are required prerequisites; dashed are recommended or helpful. Lower rows are more foundational. Click any box to jump to that concept.