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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21 views

Delaunay Triangulation on Convex Polytopes — Uniform Sampling

My goal is to uniformly sample from a convex polytope. I know that for the simpler case, where I have to uniformly sample from a simplex, I can use Bayesian Bootstrap, discussed in these posts: ...
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1answer
33 views

Simulating Random Vectors Based on Conditioning

I'm working on a project where I need to simulate random vectors $(Y, X_1,\dots,X_n)$ in order to understand the joint distribution $f(y,x_1,\dots,x_n)$. I wish to simulate enough random vectors so ...
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0answers
12 views

SRSWOR involving Weighting

A Simple Random Sample Without Replacement (SRSWOR) survey is conducted that included too many women and not enough men in the sample In the resulting weighting, each female is given a weight of $1$ ...
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27 views

Gibbs sampling truncation for contrastive divergence

I am following Yoshua Bengio's Learning Deep Architectures for AI and at page 31 there is a phrase that confuses me. Starting by lemma 7.1 in the same page: Lemma 7.1. Consider the Gibbs chain ...
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35 views

How to proceed with this simple proof?

If $$\alpha_k = \sum_l a_l \ \ g((k-l)T-l\Delta T)$$ $$s_k = \sum_l \alpha_l \ \ q((k-l)T+k\Delta T)$$ where $a_l \in \pm1$ and $g(t) = \frac {\sin(\pi t/T)}{\pi t/T}$ and $q(t) = \frac {\sin(\pi ...
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2answers
30 views

Sampling from the von-Mises Fisher distribution?

This topic has already been tackled on this website (here). But, unfortunately, no clear cut answers were given. In (Wood,1994), there is apparently a rejection algorithm for sampling from this ...
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0answers
39 views

Sampling with no duplicates

I am sampling a population of unknown size and unknown distribution. The sample will be taken over distinct time intervals, but I have to reject any duplicates in the given time interval. The sample ...
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1answer
17 views

Non-integer $n$ in sample size problem

Setup Consider a sample size determination problem with the maximization of expected utility approach (as in Lindley 1997). Let $\theta$ be the state, $x=(x_1,\dots,x_n)$ a sequence of $n$ iid ...
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35 views

Is there an exact solution for this resampling (synchronization) problem?

I want to know if there is an exact solution for the following problem and how to approach solving it: I have a discrete-time signal where the Nyquist theorem is satisfied: $$ r_k = \sum_i ...
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19 views

Formula for sampling with random replacement

I wonder if the following problem and its analysis is already known? Suppose Alice and Bob play a game where Alice has an urn with N hollow balls, all balls numbered uniquely by some integer number ...
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23 views

find the minimum sampling frequency at which the following signal must be sampled to avoid aliasing

find the minimum sampling frequency at which the following signal must be sampled to avoid aliasing $x(t)=0.5+10\cos(2 \pi t)+20\sin(50 \pi t)$ my work The frequency of the analogue signal can be ...
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31 views

Combining Sample Means and Variances

Let us assume we have several samples of unknown size but known mean value $\mu_{i}(x)$ and known variance $\sigma_{i}^{2}$. Now we want to calculate the mean value and variance for the total ...
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26 views

Dvoretzky–Kiefer–Wolfowitz inequality holds for discrete distributions?

I am wondering whether Dvoretzky–Kiefer–Wolfowitz inequality holds for discrete distributions? Any comments or references would be greatly appreciated.
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21 views

Proving that each element in reservoir have equal probability of been selected in reservoir sampling?

Here is the description of the algorithm and proof of the correctness The algorithm creates a "reservoir" array of size $k$ and populates it with the first $k$ items of $S$. It then iterates through ...
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23 views

problem about graph of auto-correlation for wide-sense stationary process?

I have the answers but I don't understand the idea and how it can be solved ? please clarify and help me to understand it thank you all
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11 views

distribution of non-central chi random sample

Suppose that $X_1,X_2, \ldots, X_n$ is a random sample from a non-central chi distribution with $1$ degree of freedom. What is the distribution of the sample variance of $X_1,X_2, \ldots, X_n$?
1
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1answer
25 views

Law of large numbers with correlated variables

My sample is a series of measurements of the variable $x$. Measurement t, $x_{t}$, is correlated with $x_{t-n}$. However, as n tends to infinite the correlation tends to zero. If the sample grows, ...
2
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1answer
20 views

Sampling distribution of $\frac{\bar{X}}{S}$

Suppose that I have a random sample $X_1, … ,X_n$ from a $N(0,\sigma^2)$ distribution. What is the distribution of $$\frac{\bar{X}}{S}$$ and what is it's standard deviation? Here $\bar{X}$ is the ...
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1answer
46 views

How to calculate a population mean for a normal distribution

This is for homework, but I'm a bit confused on how I can find $E(X_i) = \mu$ given a normal distribution. The question is as follows: In a farm, let $X$ denote the number of fruits harvested in a ...
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1answer
20 views

Sampling with replacement: finding all answers with one specific characteristic

I have a book, and I dont get it. We are talking about the following situation.Lets say you have 5 experiments and the sample space for each is $S = \{0,1\}$. So the total amount of possible outcomes ...
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1answer
19 views

Probability of successful sampling fron a population

Say I have a list of 100 questions from which to study for an examination. In the examination I will be asked 10 random questions from the 100 and I pass the exam if I answer 6 questions correctly. ...
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5 views

Sampling specific unit vectors

Given a unit vector $A\in \Bbb{R}^N$ and an angle $\theta$, the unit vector $P$ needs to satisfy $\left<A,P\right>=\cos\theta$. How to sample $P$ uniformly? For example: If $A = ...
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0answers
12 views

Sampling in the time domain vs. sampling in the frequency domain

If I have a sample rate of 2 seconds on a 128 second time window (64 samples total) and then I do a Fourier transform, what is my sample "rate" in the frequency domain? Will I end up with 64 ...
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22 views

Random Variables and Statistic

I'm studying Statistical Inference by Casella and I'm confused with the definitions of random variable & statistic. So let we have the probability space $(\Omega, F, P)$ where $\Omega$ is the ...
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38 views

How sample size affects confidence interval.

Suppose the weight of n primary one students has sample mean of 20KG. If n = 40, a certain percentage of confidence interval for the population mean is (15.5,24.5). Find the confidence interval if we ...
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27 views

Comparing two populations

I have sampled from two separate populations, and I want to figure out which population is better. Population 1 has an average score of 84.1 and a standard deviation of 11.8. Population 2 has an ...
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29 views

Simulating r.v.'s from a joint density by rejection sampling in R. Continued

I wish to sample variables $v$ and $w$ from the joint density $$(v+w)e^{-\frac{(v+w)^{2}}{2x_{0}}-2\mu v-(\mu -\lambda )w},$$ where $x_0$, $\mu$ and $\lambda$ can be seen as positive constant. Since ...
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31 views

Fourier transform of a 3sinc^2(100πt)

I'm currently studying for an exam, and I'm not sure the textbook's answer for the fourier transform of 3sinc^2(60πt) is correct. For this question, I incorporated the duality property. Below is my ...
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0answers
26 views

MSE for the Method of moments estimator of variance

would appreciate some help here please - Question: Find the MSE for the MOM estimator of the variance $\hat{\sigma^{2}} = \frac{n-1}{n}S^{2}$ based on a random sample from a normal distribution. My ...
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0answers
23 views

How can I make the mean of samples be approximately equal to the mean of actual continuous signal?

Suppose there is signal f(t) that is continuous and periodic. It is known that this f is T-periodic. (but it's not necessarily a single cosine f(t).( I'd like to make the mean of samples be ...
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1answer
39 views

Probability of occurrence in a subset of a population [closed]

If 100 individuals i.e. 2% of a population totalling 5000 people, have a certain characteristic, what is the probability of two or more persons within a subset of 10 persons, taken from that same ...
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24 views

Sampling from conditional distiribution

I want to sample from condtional distribution given by formula: $$ P[T_{n+1} =t| T_n=t_n] = ...
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1answer
31 views

Chi distribution and sample variance

Suppose that the height (in cm) of randomly selected male is distributed according to normal distribution with parameters $\mu = 175$ and $\sigma = 5$. We pick a simple random sample of size ...
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27 views

Sampling from weighted sum distribution

I have $n$ probability density functions $p_1, \ldots, p_n$, which I am able to sample from. How to sample from a weighted sum of these PDFs $$c_1 p_1+ \cdots+c_n p_n$$ given that $c_1+ \cdots+c_n=1$? ...
1
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1answer
66 views

Uniform lattice sample inside a particular convex polytope

[update]: hardmath suggests using tools from linear programming. This looks like a good idea indeed. I can now tell that my feasible set is described by: $Set = \{d \in \mathbb{N}^c, -B.d\leqslant ...
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1answer
107 views

Finding the minimum sample size of an opinion poll

I have encountered the following problem in a textbook,: Assume that 28 % of voters favored party A at some point. A later opinion poll gave a result of 30 % of voters favoring party A. What is ...
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2answers
73 views

Understanding Sufficient statistic.

A sufficient statistic for a parameter is a statistic that captures all the information about a given parameter contained in the sample. My question: Is the above sentence correct. (I think it is). ...
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2answers
21 views

Checking whether the given statistic is sufficient

A random sample is drawn from a Bernoulli distribution with $X_i = 1 $ with unknown probability $p$ and zero otherwise. Examine whether the following statistics are sufficient for the parameter $p$ ? ...
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14 views

Random assignments with 95% confidence of at least $K$ duplicate assignments

I'm running an experiment online. Of my $N$ test questions, each participant sees $M$ (randomly selected, $M < N$). If I want a minimum of $K$ responses to each question, how can I calculate a ...
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24 views

Help Determining a Statistically Significant Sample Size

I am planning on conducting an advertisement test for a website. Basically, I want to know whether visitors to my website would simply just return and convert regardless of seeing an ad or not. I will ...
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0answers
18 views

Importance Sampling Distribution

I have an infinite set of events and these event are either ture or false. I perform a monte carlo simulations to find the probability of an event being true. Now I have the knowledge that $A$ % of ...
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1answer
31 views

Resampling Probability

I've had a student working on some resampling problems. Here's a question I've posed to her: M consecutive draws of size K are taken from an urn with N balls. Balls are replaced between draws. ...
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5 views

Why is importance sampling always framed as calculating E(h(x))?

In all of the tutorials I've seen, importance sampling is always framed as a way to calculate: $$E(h(x)) = \int h(x) f(x) dx \qquad x \sim f$$ I don't understand why it is not framed as a more ...
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0answers
7 views

Statistics sampling on over-lapping categories.

I got a finite population. (e.g. a pool of files) The objective of the audit is to determine whether the files are in order. I need to audit the files for 5 different category on the population. Each ...
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429 views

Sampling Distributions

Parts being manufactured at a plant are supposed to weigh 40 grams. Suppose the distribution of weights has a Normal distribution with mean 40 grams and standard deviation 2 grams. Quality control ...
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1answer
57 views

Sampling demonstration using combinatorics

Suppose that I have a finite population of A's and B's, with properties: Population size: $n$ There are $n_1$ A's and $n - n_1$ B's (so that $p = \frac{n_1}{n}$, $q = \frac{n - n_1}{n}$) I'm ...
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1answer
14 views

hypergeometric distribution and random sampling

Is there any simple and fast algorithm (to be implemented in Javascript) to obtain a sample from the hypergeometric distribution? My needed sample size is very large (100,000,000).
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2answers
62 views

Chance to pick n balls out of N numbered ones where one ball is a specific number (without replacement, order doesn't matter)

An urn contains 120 balls numbered 1 to 120. Find the probability of choosing 3 balls without replacement that includes one ball numbered “11”. My attempt: Picking "11" would have the probability ...
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2answers
57 views

Basic sampling of joint random variables

If random variables $X \in \mathcal X$ and $Y \in \mathcal Y$ are sampled jointly from a target distribution $\pi$, i.e. $(X, Y) \sim \pi(x, y)$, is $X$ sampled from the correct marginal? In other ...
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79 views

Monte Carlo sampling and Kolmogorov–Smirnov test in practice

I have two deterministic algorithms, Algorithm 1 and Algorithm 2. The first has $m$ inputs and one output, and the second has $n$ inputs and one output. The distributions of the inputs of the ...