# Questions tagged [independence]

For questions involving the notion of independence of events, of independence of collections of events, or of independence of random variables. Use this tag along with the tags (probability), (probability-theory) or (statistics). Do not use for linear independence of vectors and such.

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### How to prove this relation for Kendall's distribution function (or Kendall's measure)

Kendall Distribution Function (Nelsen, 2006, p. 163) Or Kendall Measure (Salvadori et al., 2007, p. 148) Or Kendall Function (Joe, 2014, pp. 419–422) is the cumulative distribution function (CDF) of ...
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### What is the formula for PMF from adding independent zero-modified negative binomial random variables?

Let $X$,$Y$,and $Z$ be independent identical zero-modified negative binomial (ZMNB) random variables, then how would the probability mass function (PMF) be calculated? $$P(X + Y + Z = k) = ?$$ For ...
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### Change of variable in conditional density function

I am reading a paper that makes the following argument: Define $\psi_i := E[x_i | \mathcal{F}_{t-i}]$ and $\epsilon_i := \frac{x_i}{\psi_i}$, where we assume that $\epsilon_i$ is independent and ...
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### Probability that at least one event happens (dependent events)

Problem description Assume we have a bag filled with marbles of two different colors, red and blue. Our goal is to be able to pick out at least one red marble by picking out the least amount of ...
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### $X$ $Y$ are independent so are $f(X)$ and $f(Y)$ if $f$ is continuous

Assume you have a sequence of random variables $X_1,X_2,\ldots,X_n$ taking values in a (separable) metric space $\mathcal{X}$. Moreover assume $f:\mathcal{X}\rightarrow \mathbb{R}$ is continuous. Then ...
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