# Questions tagged [sampling-theory]

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### Find the sample size $n$ for a stratified sampling method

Let’s say we have a finite population $N=5000$.We have divided the population into 5 subgroups according to a risk characteristic “very low risk”,”low risk”,”medium risk”,”high risk” and “very high ...
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### Conditions and techniques for discretizing a real function

Sampling theorem states: If a function $x(y)$ contains no frequencies higher than $B$ hertz, it is completely determined by uniform samples taken at less than $1/2B$ units apart. Original sampling ...
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### Optimal sample length - optimal experiment planning

I have a measurement signal with a length of, say, 1 million samples. On the signal, I use digital signal processing techniques to obtain information that interests me. I noticed that I don't have to ...
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### Number of samples in SRSWR and SRSWOR

In a population of N units, if a sample of n units is chosen, the number of possible samples is N ^ n (SRSWR) NCn. (SRSWOR) Taking an example, let there be a population (a,b,c) and let a sample of ...
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### Sampling theory (signal processing): why is multiplication by the dirac comb used to represent sampling?

Wikipedia (and other sources) make the following claim (from https://en.wikipedia.org/wiki/Dirac_comb): The claim is that multiplying any function by a Dirac comb transforms it into a train of ...
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### Problem regarding drawing balls by SRSWOR

A box contains 2016 balls labeled 1, 2, 3, . . . , 2016. Two balls are selected at random by sampling without replacement. Let X and Y be the labels on the first ball and the second ball, respectively....
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### What is the average length of a line inside the unit square?

This question lies in the chapter exercise of chapter 14 Sampling of book: Fundamentals of Computer Graphics by Peter Shirley and Steve Marschner. Although this is not mentioned in the question but I ...
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### Help with a t-Student distribution

In class, the professor has left us with the following exercise: Given two samples $(X_1,...,X_8)$ and $(Y_1,...,Y_{15})$, where $X\sim N(\mu_1,\sigma_1)$ and $Y\sim N(\mu_2,\sigma_2)$, all parameters ...
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### Can the definite integral of zero valued function be non-zero?

I am trying to understand the Importance Sampling Technique (IS) for rare event simulation. I use the this tutorial. On page 5, it is written: "...That is, let g be another probability density ...
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### Groups of random binary vectors with small intra-group and large inter-grup similarity

Is there a formula for simultaneously sampling N random binary vectors, each of length M, with the property that the distribution of the M binary values is distinct between groups? The N vectors in ...
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### Sampling distribution of sample mean

We are sampling $Y_1,\dots,Y_n$ without replacement from the population of size N with $Y\sim$ Bernuolli($\mu$). So what will the asymptotic distribution of $\bar(Y_n)$ would be? Since CLT only ...
22 views

### How to determine Two-tailed or One-tailed test?

For example while testing difference of two means $\mu_1-\mu_2$ as the numerator in the test statistic, is this left-tailed or right tailed? What if I take $\mu_2-\mu_1$ in the numerator? Will the ...
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### Standard error for difference of standard deviation

Since under the Null hypothesis, $\sigma_1=\sigma_2$, why is this not applied in the standard error formula? Shouldn’t it be $\sigma_1=\sigma_2=\sigma$?
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### How to distinguish between sample and population?

Suppose if we have two big populations with some attribute A, the population proportions of this be $P_1$ and $P_2$ and sample proportions with regards to this same attribute be $p_1$ and $p_2$. If we ...