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Find the CDF if $P(X=1)=\frac{1}{2}$ and $P(a<X<b|X\ne1)=\frac{b-a}{2}$ for $0\leq a<b\leq2$

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#probability #solution-verification #cumulative-distribution-functions
37
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If for all $t\in\mathbb R,F_X(t)=0$ or $F_X(t)=1$, then there exists $\varphi\in\mathbb R$ with $P(X=\varphi)=1$

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#probability #probability-theory #cumulative-distribution-functions
119
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Cumulative distribution function derivation

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#probability #cumulative-distribution-functions
477
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lower limit of the Cumulative distribution

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#probability #probability-distributions #cumulative-distribution-functions
582
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Minimum and maximum of series of random variables

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#probability #probability-distributions #random-variables #cumulative-distribution-functions
57
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How to prove the following result about CDFs?

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#probability-theory #probability-distributions #cumulative-distribution-functions
802
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Mathematically finding the bounds of a CDF for a random variable

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#probability-distributions #density-function #cumulative-distribution-functions
30
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Understanding these probabilities

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#probability #probability-distributions #cumulative-distribution-functions
88
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Finding CDF of Composition of random variable and real function

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#probability #solution-verification #cumulative-distribution-functions
114
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Finding the joint distribution of two dependent random variables given conditions

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#probability #probability-distributions #conditional-probability #bivariate-distributions #cumulative-distribution-functions
327
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Intuitively, *why* is the joint density function zero when the joint cumulative function is constant/single variable?

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#probability #density-function #bivariate-distributions #cumulative-distribution-functions
118
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Why is the function $y(x) = \frac{1}{x}$ not a distribution?

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#smooth-functions #cumulative-distribution-functions
131
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Proving something similar to $\mathbb E(g(X)) = \int_0^\infty g'(x) P(X>x) dP$

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#probability-theory #expected-value #multiple-integral #cumulative-distribution-functions #fubini-tonelli-theorems
1.5k
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PDF of $\min$ and $\max$ of $n$ iid random variables

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#probability #probability-theory #probability-distributions #solution-verification #cumulative-distribution-functions
94
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cumulative distribution function, inverse and quantile

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#probability #quantile #cumulative-distribution-functions

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