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Prove that $f(x)=\frac{3}{4}(2x-x^2)$ if $x \in (0,2)$, $f(x)=0$ otherwise, is a density

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#probability-theory #density-function
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Intuitive understanding of integrating a cumulative distribution function

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#integration #density-function
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Understanding dense discontinuities

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#probability #density-function
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Random number generator with given density:

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#integration #probability-distributions #density-function
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Finding a PDF from a MGF

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#probability-distributions #density-function #moment-generating-functions
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Understanding functional equation for order statistics

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Inverse Transform Method for a pdf

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Stupid question about Law of the Unconscious statistician

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Density of Adding Two Independent Uniform Random Variables

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176
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How to know the probability distribution without knowing the probability density?

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Related PDFs of Continuous Random Variables

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145
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Generalizing a proof for the density of stopped subordinators

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#proof-verification #stochastic-processes #stopping-times #density-function #levy-processes
266
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The naive kernel density estimator definition

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#probability-distributions #random-variables #estimation #density-function
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$X$ chosen from set $\{1, 2, 3, 4, 5\}$ and $Y$ chosen from $\{1, ... X\}$, find joint and conditional p.m.fs

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#probability #conditional-expectation #convolution #density-function
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Approximation of $\left(1-x^2\right)^{\tfrac{n-3}{2}}$ to Normal distribution

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