# Questions tagged [probability-distributions]

In probability and statistics, a probability distribution assigns a probability to each measurable subset of the possible outcomes of a random experiment, survey, or procedure of statistical inference.

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### What's the probability of two independent events in time domain?

Suppose there are two independent events A and B. The probability that A or ...
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### Estimating the size of the remainder in a random partition

Pick a sequence of real numbers $x_i$ as follows. Put $x_0=1$. If $x_i$ is chosen, then pick $x_{i+1}\in[0, x_i]$ according to the uniform distribution. Obviously we have $x_i\rightarrow 0$ with ...
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### Given two probability density functions find a number that satisfies a given equation

I have a problem for which I either need a proof or a counterexample. We are given two discrete random variables $x_1$ and $x_2$ in $[0, n]$ where $F_1(x)$ is the probability of $x_1\leq x$, and ...
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### What is $\sum_{k=0}^{+\infty}{k⋅p(k;\mu_1,\mu_2)}$, where $p$ is the pmf of Skellam distribution?

The Skellam distribution is the discrete probability distribution of the difference $N_{1}-N_{2}$ of two statistically independent random variables $N_{1}$ and $N_{2}$, each Poisson-distributed with ...
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### What is the expected minimum total matching distance between two partitions of identically and independently distributed points?

Suppose a square $[0,1]\times [0,1]$ in which $N$ vehicles $V_i$ and $N$ riders $R_i$ are distributed identically and independently (say, uniform distribution), a bipartite matching (or a permutation, ...
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### Probability density from standard domain - I

Pick $x+iy$ at random with respect to hyperbolic measure from $\{z:|z|\geq1,|\mathcal R(z)|\leq\frac12\}$. What does the probability distribution function of $\frac1{\sqrt y}$ look like?
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Is there a method using random matrix theory and NOT using free probability to determine the asymptotic eigenvalue distribution of the random matrix $\mathbf{M}=\mathbf{X}_1+ \mathbf{X}_2$? where: $\... 1answer 119 views ### Log concavity of the maximum of dependent Gaussians Let$Z_1,\dots,Z_n$be dependent Gaussian random variables. Is it true that$X=\max\{Z_1,\dots,Z_n\}$has a log-concave distribution function? This is true for the independent case, but is it true in ... 1answer 188 views ### Is the normal product distribution sub-gaussian? Consider the normal product distribution, which is the distribution of the product of two or more independent normal variables. Particulary, focus in the case where the multiplied normal variables are ... 1answer 120 views ### Tail probability of random projection Suppose$v\in R^n$is a constant unit vector.$P_l$is a random projection matrix to an$l$dimensional subspace of$R^n$which is uniformly sampled from$G(l,R^n)$which is the collection of all$l$-... 1answer 74 views ### Bivariate Poisson-Binomial distribution Suppose you have$100$coins whose probabilities of obtaining the outcome "head" are$p_1,\ldots,\,p_{100}$. These probabilities are not necessarily equal each other. Consider the following random ... 3answers 315 views ### Distribution of sum of two permutation matrices Determinant and permanent of sum of two$n\times n$permutation matrices can be arbitrarily different. What is the distribution of determinant of sum and difference of two$n\times n$permutation ... 0answers 51 views ### Compare KS test and Wasserstein distance or Earth mover's distance I have tried the following question in couple of exchange sites but I did not get any views or reply. I am asking here as I am kind of desperate for the answer, please be considerate. Any suggestion ... 0answers 132 views ### Closed-form formula for Wasserstein distance between uniform discrete distribution and discrete distribution with same support Let$x_1,\ldots,x_n$be$n \ge 1$distinct points in$\mathbb R^d$and consider two discrete distributions on these points$\mu = (1/n)\sum_{i=1}^n\delta_{x_i}$, and$\nu = \sum_{i=1}^n\nu_i\delta_{...
I'm in trouble trying to generate samples following a particular distribution which is not numerically known perfectly. Let us consider a $R^n$ space provided with an orthonormal base \$( e_{1},...,e_{...