# Questions tagged [random-variable]

A random variable or stochastic variable is a value that is subject to chance variation (i.e., randomness in a mathematical sense).

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### Does $f(X) = X$ imply $f$ is identity?

For a random variable $X$, does $f(X) = X$ imply that $f(.)$ is the identity function, at least over the support of $X$?
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### Joint distribution of X and Y given both of X and Y are random variables from normal distribution, but X and Y are correlated with ${\rho}$ [closed]

The difference between being two independent random variables and being uncorrelated?
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### Can VAE treat each pixel rather than image as random variable? [closed]

As I understand, the VAE encoder outputs vector of means and variances with each element corresponding to one image in the X training set. This means that we treat each image as one random variable . ...
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### Empirical Histogram and PMF

I am taking an introductory course on statistics/probability and there's a concept that I am confused with. That is the difference between empirical histogram vs PMF. First off, let's use the example ...
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### Binomial glmm with a categorical variable including zero cell [duplicate]

I am analyzing the data using generalized linear mixed-effect models (GLMM) using the lme4 software package (Version 1.1-30 in R; Bates, Maechler, Bolker, & Walker, 2022). The model includes 2 ...
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### Possible to have independent observations without random sampling?

Is some form of random sampling required for observations to meet the "independence" assumption of various types of regression analysis and hypothesis testing? My data (fish counts, without ...
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### Analyzing data from a non-randomized sampling design (ecological monitoring)

I have 2 questions about analyzing data that was not randomly sampled from a population. I work with "ecological monitoring" data that involves repeatedly taking measurements from the same ...
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1 vote
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### Choosing a proposal density g(x) for $f(x)= {\Large \frac{e^{x}}{(e-1)} }$ [closed]

In finding an proposal distribution function $g(x)$ for the following function: $f(x)= {\Large \frac{e^{x}}{(e-1)} }$ where $0 \leq x \leq 1$ Tested with $$x^2+1, 1/x+1$$ and other variations, but ...
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### Confused about random variables and time series

I have this two practical (with R) exercises for my exam: Using $\chi^{2}$ to test (goodness-of-fit) if fluctuations in wind speed are Gaussian. Calculating Lagrangian time scale for wind speed. In ...
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### What are the names of random variables in conditional probabilities?

In a conditional probability like p(A|B), what A and B are called?
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### Does k moments imply k + $\epsilon$ moments?
If you have a random variable $X$ such that $\mathbb{E}(|X|^k) < \infty$, does it follow that $\mathbb{E}(|X|^{k+\epsilon}) < \infty$ for some (potentially small) $\epsilon > 0$? If not, ...