# Tagged Questions

Questions about the statistical process of sampling from a population, in order to obtain information for use in statistical learning, estimation, hypothesis testing about some population or process.

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### What is the distribution of gaps?

Randomly select $n$ numbers from the universe $\{1,2\dots,m\}$ with or without replacement, and sort the numbers in ascending order. We can get a list of number $\{a_1,a_2,\dots,a_n\}$, and then we ...
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I am studying statistics and I am wondering when it comes to standard error or a sampling if the calculation changes when there are weights added. I have a weighted mean: $$\mu_{w} = \dfrac{\sum_{i=... 1answer 92 views ### Generation of random variable from a complicated CDF Suppose I am given a CDF of a distribution, given by F(x) ∝ \int_0^1 x^y e^{-y} dy. Here,'x' ranges from 0 to 1. How do I generate a random variable from this distribution? 1answer 928 views ### Uniform sampling of points on a simplex I have this problem: I'm trying to sample the relation$$ \sum_{i=1}^N x_i = 1 $$in the domain where x_i>0\ \forall i. Right now I'm just extracting N random numbers u_i from a uniform ... 1answer 3k views ### Probability to choose specific item in a “weighted sampling without replacement” experiment Given n items with weight w_n each -- what is the probability that item i is chosen in a k-out-of-n "weighted random sampling without replacement" experiment? Can a closed-form solution that ... 3answers 1k views ### estimate population percentage within an interval, given a small sample Given a small sample from a normally-distributed population, how do I calculate the confidence that a specified percentage of the population is within some bounds [A,B]? To make it concrete, if I ... 1answer 284 views ### Sampling Q uniformly where Q^TQ=I (This is related to this question) Q \in \mathbb{R}^{n\times k} is a random matrix where k<n and the columns of Q are orthogonal (i.e. Q^T Q = I). To examine E(QQ^T), I conducted monte ... 2answers 87 views ### What does it mean to sample, in measure theoretic terms? Suppose I have some random variable X defined on some probability space (\Omega, \mathcal{F}, \mathbb{P}). What does it mean, in measure theoretic terms, to draw a sample from X? When \Omega ... 4answers 161 views ### Sample: don't confuse measurements with actual values? In Wikipedia's article on Sample there is the following remark: ''Note that a sample of random variables (i.e. a set of measurable functions) must not be confused with the realizations of these ... 2answers 104 views ### Independence of Poisson random variables coming from Poisson sampling Context: Let x \in \mathbb{R}^n be the unknown probability vector of a finite discrete distribution X. We are able to sample X and we want to learn x. Poissonization: Each observation ... 2answers 110 views ### Why is there a difference between a population variance and a sample variance Sorry if this answer is simple but I was wondering why is there a difference between a population variance and a sample variance? I understand The variance is calculated as:$$\text{Var} = \frac{1}{...
Given spherical coordinates on a unit sphere, imagine a spherical quad defined by two ranges $[\phi_0,\phi_1]$ and $[\theta_0,\theta_1]$. If you have a globe, for example, the grid formed by the ...