# 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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### Use Importance sampling for multimodal and multivariate distribution draws, how to choose proposal distribution?

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_{...