# Tagged Questions

22 views

### Difficult Survey Sampling question

Question: A Secretary of State wants to survey the primary owners of motorcycles registered in the state to estimate the proportion who want the license plates redesigned. (Primary owner means that ...
59 views

### Uniform sampling with replacement item frequency

Suppose we are sampling from $N$ distinct items uniformly with replacement $M$ times. What can be said about the distribution of frequencies of items drawn? For example, if I sort all the frequencies ...
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### Sampling with an “oversampling” factor, in K-Means||

I'm trying to understand K-Means||, a scalable version of K-Means++, which itself is an "improved" version of the clustering algorithm K-Means. Please find here the link to K-Means|| paper ...
61 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 $\Omega$ ...
69 views

### The mean and variance of the sample median

The population and the median of a sample sized $2k+1$ should have the same mean and variance. Why is that? Will the result still be so tidy for a sample sized $2k$?
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### Sampling uniformly from n-sphere using spherical coordinates

It has been explained here why sampling from n-sphere is not achievable with naive parametrization. And it explains how to correct it for 3 dimensions. Can somebody please guide me what is the correct ...
83 views

### Is it possible to sample the Dirac delta function?

The Dirac delta function can be a probability measure with the unit/Heaviside step function as its cumulative distribution function. Is it possible to sample such a distribution? If a random variable ...
87 views

### Maximum likelihood estimation - why is $\mathcal{L}$ not the joint pdf?

Here's an excerpt from my notes: Define the likelihood function: $$\mathcal{L}(\vec{x};\theta)=\prod_{i=1}^{n} f(x_i;\theta)$$ Where $f$ is the pdf of the distribution we're sampling the $x$'s ...
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### Suitable change of measure with importance sampling

I'm working on a project on Importance Sampling. When one tries to estimate the small probability $\alpha:=\mathbb{P}(X \in A)$, one can do a change of measure. There is change of measure which ...
54 views

### Continuous random sampling with replacement.

Construct a set $s\subseteq[0,1]$ by sampling points in $[0,1]$ with uniform probability density $x\leq1$ so that $|s|=x$. Interpret this as a sampling frame during which data is captured. Now, ...
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### 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 ...
163 views

### Sampling from discrete probability distribution from first principles

I have a set $S=\{a_1,a_2,\dots,a_n\}$. The probability with which each of the element is selected is $\{p_1,p_2,\dots,p_n\}$ respectively (where of course $p_1+p_2+\cdots+p_n=1$). I want to ...
45 views

### Bias in Resampling

I'm currently doing some work with Particle Filters, a sampling-based method for computing expectations of functions with respect to dynamic (ie: time-variant) random variables. For example, consider ...
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 ...