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∑MathAdvanced

Lebesgue Integration

Lebesgue integration measures how much time a function spends near each value and adds up value × size of the set where it occurs.

#lebesgue integral#riemann integral#measure theory+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
∑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