# Questions tagged [sampling-theory]

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### A sample of size $n=80$ is drawn from a population of size $N$. The sample size is divided into two parts .

A sample of size $n=80$ is drawn from a population of size $N$. The sample size is divided into two parts and samples are drawn independently from both the parts.The one-fourth sample is drawn by ...
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### Determining Normality With Large Samples

I am taking in some files and I must determine if the data sets are normally distributed (yes, within a certain degree of certainty because it cannot be proven only disproven). My data sets are quite ...
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### Why is sampling distribution of means's standard deviation sd/sqrt(n)?

I'm so used to seeing standard deviations being the sqrt of the entire formula so it's weird to me to see a SD that is defined as sd/sqrt(n). Can someone explain why?
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### Estimation population size using sampling - real life probability

I have come across similar questions like this previously but I just can't get my head around a correct method Clive catches 50 bees from the beehive and marks each bee with a dye then lets them go. ...
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### What does it mean that a distribution is hard to sample from?

I'm currently studying about sampling methods, and some terminology that has arisen is that a distribution is "hard to sample from". What does this mean? My current intuition is that the ...
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### Notations question regarding the equation for sample mean and variance

Let $X$ be the outcome of a chance experiment with $E(X) = \mu$ and $V(X) = \sigma^2$. When $\mu$ and $\sigma^2$ can be estimated by repeating the experiment $n$ times with outcomes $x_1, x_2,...,x_n$,...
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### How to infer the underlying distribution of a statistic (Bayesian inference?)

I have a list of approximately 30,000 venues in a major US city. These venues hold all kinds of events, sports, conferences, concerts etc. I want to know the distribution of the 'capacity' of these ...
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### Continuous random sampling - random selection of units with average frequency

Scenario: Multiple agents process orders simultaneously. Orders are not shared between agents. Each agent is assigned a sampling percentage. Let say agent A has sampling percentage of 10% and B has ...
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### How to sample the position of many particles?

In Density Functional Theory, there are many types of trail variational wave functions. I have a question from the numerical viewpoint: when I have the 1D density functions, and the $N$-dimensional ...
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### prove that $(n-1)(\frac{1}{n} \sum_{i=1}^{n}\hat{\sigma^2_{-i}}-\hat{\sigma^2})=-\frac{S^2}{n}$ in i.i.d sample(the factor n-1 in the jackknife bias)

let $x=(x_1,\cdots,x_n)$ are n independent samples from unknown distribution. The Jackknife Samples are selected by taking the original data vector and deleting one observation from the set. Thus, ...
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### Sampling distribution of a functional T

While studying the bootstrap method, I came across with the following definition of the sampling distribution of a functional T: Let's say $X_1,...,X_n$ are i.i.d with distribution function $F$, then ...
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### sampling a connected graph to a smaller connected graph

I have a graph $G$ which has $n$ nodes and $\alpha*(n^2-n)/2$ edges (so the chance of having edge $(i,j)$ is $\alpha$). The graph is connected which means that if we calculate the number of components ...
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### Rigorous Meaning of “Drawing a Sample” $\omega$ from a Probability Space $(\Omega, \mathcal{A}, \mathbb{P})$

Let $(\Omega, \mathcal{A}, \mathbb{P})$ be a probability space. What does it mean (in the most formal and rigorous sense possible) to "draw a sample" $\omega \in \Omega$ from this space? Intuitively, ...
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### Picking path at random in DAG graph with probability equals to path weight.

I'm refering to the following paper: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.329.3653&rep=rep1&type=pdf. There is a lemma states: Let $G$ be a directed acyclic graph with ...
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### Let $V_1$ be the variance of the estimated mean from a stratified random sample of size $n$ with proportional allocation.

Let $V_1$ be the variance of the estimated mean from a stratified random sample of size $n$ with proportional allocation. Assume that the strata sizes are such that the allocations are all integers....
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