# 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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### Correct or Not? Probability and Geometry [closed]

A stick of length $1$ is broken into two pieces of length $Y$ and $1−Y$ respectively, where $Y$ is uniformly distributed on $[0,1]$. Let $R$ be the ratio of the length of the shorter to the ...
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Assume that $p$ and $q$ are two distributions and $x$ and $z$ are two random variables. Can the following term (which appears in the paper Auto-Encoding Variational Bayes) be further simplified? $$\... 1answer 27 views ### random factos really significant? I have some confusion about random factors inclusion or not. I've used the function glmer.nb of the library MASS to analyse the effects of two fixed factors (temperature: 2 levels and salinity:3 ... 1answer 48 views ### Probability of getting a negative mark if one chooses options randomly in a MCQ question with negative marking In a test with 100 multiple choice questions, a student chooses to pick an option randomly. There are four options for each questions. Answering a question correctly will give the student 1 mark, ... 1answer 46 views ### Decomposing a random variable into marginals and copula I’m having trouble getting understanding how to actual construct a copula, from my understanding it captures the purely joint features of a joint distribution. I’ve been working with the following ... 1answer 35 views ### Probability of having an increasing trend in normal variates Let x\sim N(\mu,\sigma) and x_i is ordered instances of random variate of x for i=1...n. What is the probability that the series is in increasing (or decreasing) order? The problem is finding ... 1answer 29 views ### Perpendicularity of random variables? I am reading Bechavod et al. (2017) , and at page 3 there is written: In the example, each data point lies in X = (X_1,X_2) = \{0, 1\}^2 and has two features—X_1 = A is the protected ... 1answer 50 views ### Supremum of parameterized random variables over compact set Suppose that we have a parameterized real-valued discrete stochastic process x(t) :=\{x_k(t)\}_{k=1}^\infty, such that t assumes values in a compact set T\subset \mathbb{R}^d for some finite ... 0answers 38 views ### Can two random variables be independent in some basis and dependant in other? If some random variables forming N dimensions are dependant on each other is it possible that in a different coordinate system they'd be independent? For example if (X, Y) are two dependent RVs is it ... 0answers 29 views ### Decomposition random variable with conditional expectation [closed] Why given some information set I, any random variable x_t can be decomposed into the sum:$$x_t = E(x_t | I) + v_t  where $E(v_t | I) = 0$. I'm looking for a clear proof.
Let $X_1$ and $X_2$ be iid non-central t random variables. I'm interested in the question: what is the distribution of $X_1 - X_2$? i.e. what is the distribution of the difference of two iid ...