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Diff — Random variable

Revision #1523 → #1845 · back to history

modifiedDiscrete random variabled4e7d36f5303
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noteDiscrete distributions are captured by `PMF`, but `Mathlib` has no class `IsDiscreteRandomVariable`.Discrete distributions are captured by `PMF`, but Mathlib has no class `IsDiscreteRandomVariable`.
modifiedProbability distribution of a random variablef90672f5ec1d
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noteThe law of `X` is `Measure.map X ℙ`, and `ProbabilityTheory.HasLaw` packages this.The law of `X` is `Measure.map X ℙ`, packaged also via `ProbabilityTheory.HasLaw`.
modifiedDensity transformation under invertible differentiable g6cdf72fd63f4
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mathlib.moduleMathlib.MeasureTheory.Function.JacobianMathlib.MeasureTheory.Function.JacobianOneDim
modifiedExample 2: exponential distribution via transformation88dec761ac15
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mathlib.declMeasureTheory.pdf.IsExponentialProbabilityTheory.exponentialPDF
noteExponential distribution is defined, but this specific transformation example is not formalized.Exponential distribution is defined via `exponentialPDF`, but this specific transformation example is not formalized.
modifiedAlmost sure equality5e7e3e383ad5
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mathlib.moduleMathlib.Order.Filter.BasicMathlib.Order.Filter.Defs
addedProbability mass function95b81011c855
addedPushforward measure (law of a random variable)4ce82714ac89
addedProbability density functionf97dfd83102a
addedRadon–Nikodym derivative75f4d8492557
addedVariance and standard deviation0b7647e4f6a1
addedMoment generating function7aa2c811fe33
addedLaw of large numbersb9d24d9c6484
addedCentral limit theorem0a0bd7f2f441
addedConvergence of random variables9877706534a8