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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Statistical analysis for a within-subjects design with a randomly varying factor
I have a statistics/data analysis question. I am conducting a study in which participants view and rate how much they like different pictures. I am interested in several within-subjects factors. Each ...
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Dependent and independent variables in logistic regression
Sometimes in observational studies in the health sciences we have a lot of variables, all of them considered as random variables. Is it possible that variables that are considered as "independent&...
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Conditional density function for X and T(X)
Consider a continuous random variable $X$ and a function $T:\mathbb{R} \rightarrow \mathbb{R}$ that is continuous and differentiable. Given this, how can we figure out the conditional density function ...
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Expectation and Kronecker product
Let $\mathbf{u} \sim \mathcal{U}(S_{\mathbb{R}^m})$ be a uniformly distributed random vector on the unit sphere $S_{\mathbb{R}^m} \triangleq \{\mathbf{u}\in \mathbb{R}^m\mid\|\mathbf{u}\|=1\}$ and let ...
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Lifting of non-reversible Markov chains for convergence acceleration
Background and motivation
Let $(\Omega, \pi)$ be a finite state space with a stationary distribution $\pi$. Consider an ergodic Markov chain on $\Omega$ with transition matrix $P$ that is irreducible ...
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Notation for Support of a Random Variable
My question may sound simple, but I am struggling to settle on a good notation for the support of a random variable when teaching the course 'Probability and Statistics'.
Suppose we have a discrete ...
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Treatment vs control when treatment is sampled from a population (no meaningful random-variable level for control cases)
Our design is between-subjects treatment vs control, but where treatment is randomly sampled from a large population of treatments of the same type. There are thousands of treatments; we sample 100, ...
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Trying to understand random variables using the function notation f(x) = y [duplicate]
Problem
I am trying to build an intuitive understanding of random variables by expressing them in the form of a function: f(x) = y. I know this isn't the conventional way of expressing a random ...
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Is there a formal threshold for when a variable is considered 'random' in statistics? What is it?
Problem
I’ve been studying the concept of a random variable, and I have come up with this understanding of what a random variable is:
“A random variable is a variable whose values are not known nor ...
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if I toss a coin twice, do I have a single random variable sampled twice independently or two independent random variables sampled once? [duplicate]
This question arose in the context of CLT, but more general answers are also warmly welcome.
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Expected Value of the Absolute Value of the Difference Between the Sum of Powers of Randomly Selected Numbers From Standard Normal Distributions
My question is similar to (and an extension of) this one.
I have a standard normal distribution. From it, I randomly select $2 \times m$ observations, divide these observations randomly into 2 groups (...
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Symmetry of linear combinations of mean 0 symmetric random vectors
Let $X = (X_1,\ldots,X_n)$ be a random vector with i.i.d. components, each symmetric around $0$, i.e. $X_i \stackrel{d}{=} -\,X_i$ for all $i$.
Given two deterministic vectors $a, b \in \mathbb{R}^n$, ...
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Confidence interval for the variance of a sample mean from a mixed model
Imagine we have a random variable: $$X = \mu + I + J + K + \varepsilon$$ where $\mu$ is a fixed unknown parameter, $I \sim \mathcal{N}(0, \sigma_i^2)$, $J \sim \mathcal{N}(0, \sigma_j^2)$, $K \sim \...
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How do you simulate the difference between two positive random variables?
I have two random variables, $Z$ and $Y$, which are strictly positive. But $Z$ is actually the sum of the two independent variables $Y$ and $X$, where $X$ is also positive and independent of $Y$. I am ...
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why does for Gaussian random vector, the property of being uncorrelated is equivalent to being independent [duplicate]
i know that if i have Gaussian random variables which are also jointly Gaussian and they are also uncorrelated then i can say that they are independent. but does this mean that i can also say:To prove ...
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