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⚙️AlgorithmIntermediate

Monte Carlo Estimation

Monte Carlo estimation approximates an expected value by averaging function values at random samples drawn from a probability distribution.

#monte carlo#expectation#variance reduction+12
∑MathIntermediate

Expectation, Variance & Moments

Expectation is the long-run average value of a random variable and acts like the balance point of its distribution.

#expectation
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#expectation
#variance
#moments
+12
∑MathIntermediate

Random Variables & Distributions

A random variable maps uncertain outcomes to numbers and is described by a distribution that assigns likelihoods to values or ranges.

#random variable#pmf#pdf+12
📚TheoryIntermediate

Probability Theory

Probability theory formalizes uncertainty using a sample space, events, and a probability measure that obeys clear axioms.

#probability measure#random variable#expectation+12
∑MathIntermediate

Linearity of Expectation Applications

Linearity of expectation says the expected value of a sum equals the sum of expected values, even if the variables are dependent.

#linearity of expectation#indicator variables#expected inversions+12