# Tagged Questions

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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### How to obtain a unimodal histogram with normal distribution (gaussian)? [on hold]

My task is to come up with a histogram consisting of $N$ bins. The histogram should show a (perfect) normal distribution. So something similar to what is shown in this image. How do I obtain the value ...
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### How to compute bounding coefficients for McDiarmid's inequality?

I am trying to understand the proof in Sec. A2 of Gretton et al.. To make the question self-contained, I summarize below the key ingredients. At the end of the post, I state my question. Given a ...
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### Upper Bound for the Difference of Even Probability and Odd Probability in Hypergeometric Distribution

Let $X$ be a random variable following the hypergeometric distribution with parameters $N,K,n$, where $$Pr(X=k) = \frac{\binom{K}{k}\binom{N-K}{n-k}}{\binom{N}{n}}.$$ To ...
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### Multimodal property of polynomial logistic distribution

Let $P(x)$ be a polynomial (of an odd degree $n$) strictly increasing on $(-\infty, +\infty).$ Then $F(x)=\displaystyle \frac{1}{1+\exp\{-P(x)\}}$ is a distribution function of a polynomial logistic ...
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### BM hitting times with exponential killing process

Assume a BM in 3d domain (infinite) with a small absorbing subdomain (cube, sphere, ect), centered at point $p_s=(x_s,y_s,z_s)$ . BM starts at point $p_0=(x_0,y_0,z_0)$ and when it riches the ...
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### Fundamental difference between Poisson Point Process and Binomial Point Process

What is the fundamental difference between Poisson Point Process and Binomial Point Process? I am evaluating a solution in a Binomial Point Process setup. If I want to evaluate that in a Poisson ...
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### Choosing a sample based on where the density function is highest

Is there a name for the following process? Say I have an absolutely continuous probability density function $f$ with compact support, and I take $k$ independent samples $x_1,\dots,x_k$ from $f$. ...
We define the $s$-sparse hypercube in $\mathbb{R}^d$ as \begin{align} \mathbb{H}_s = \bigl \{ {\bf{v}} \in \{ -1, 0 , 1\}^d \colon \| {\bf{v}} \|_0 = s \bigr\}, \end{align} where $\| {\bf v} \|_0$ ...