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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14 views

this undersample example doesn't make sense

I am studying for my DSP final and something doesn't make sense to me. If I have a continuous time signal $sin(12*pi*t)$ being sampled at T=0.1 sec. I get aliasing because I undersampled. I get ...
2
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0answers
24 views

How can I generate samples from some correlated exponentially distributed random variables?

I want to generate some samples from a set of correlated exponentially distributed random variables. I have the correlation matrix between these random variables. For multivariate normal ...
0
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0answers
29 views

Fourier Transform of a function with sinusoidal sampling

What is the relation between the Fourier Transform (FT) of $f(x)$ with regular sampling and the FT of $f(x)$ with sinusoidal sampling? In other words, it's a FT of a function composition $f\circ ...
0
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1answer
27 views

What happens to fourier transform of the sampled output of pure sinusoidal input of 26kHz if sampled with 44.1kHz sample frequency?

Because pure sinusoidal signal only contains impulses, I was wondering what happens to the fourier transform of the sample output from the sinusoidal input of $26$kHz if the sampling is done with ...
0
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1answer
41 views

Chebyshev Application [closed]

If we have a sample mean of $\overline{X} = (X_1 + X_2+\ldots+ X_n)/n$ and mean $m$ and standard deviation $s$, how large should the sample size $n$ be so that with probability $.99$ the error ...
1
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1answer
50 views

Infinite samples from uncountable sample space

I'm drawing one single sample from an uncountable sample space. I know the probability of sampling any given single point is zero. Now, what if I draw samples again and again and again, to infinity? ...
0
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0answers
21 views

Reservoir sampling from a stream containing duplicate items

Given an infinite stream with duplicate items, say, $S=\{1,2,2,1,3,2,\ldots\}$. How to uniformly sample $k$ items from its non-duplicate version, i.e., $S'=\{1,2,3,\ldots\}$? I known there is a ...
0
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1answer
30 views

Multivariate sampling of $F(x_1,…,x_n)$?

Let $$(X_1,...,X_n)\sim F(x_1,...,x_n)$$ (not independent). How can I sample from this distribution? In the univariate case, on can use $F^{-1}(u),u\sim U(0,1)$. However, in the multivariate case ...
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0answers
32 views

Simulate from a distribution using Metropolis-Hastings and Rejection Sampling?

We have covered the basics behind rejection sampling as well as Metropolis-Hastings from class, but I am not sure how to use the two in conjunction to solve the following problem: Given $\pi(x) = ...
2
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1answer
30 views

How can I uniformly draw points from an ellipsoid?

Specifically, given a positive definite matrix $A \in \mathbb{R}^{n \times n}$, how can I efficiently generate points $x \in \mathbb{R}^n$ that satisfy $x^TAx \leq 1$? I know how to do this when the ...
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3answers
79 views

Sampling Distribution; Statistics. Please verify my answer

Professor earns average $ \text{\$} 65,500$ per year with standard deviation of $\text{\$}3,500$. Random sample of $64$. a. Describe sampling distribution of sample mean $\bar{x}$ of average ...
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0answers
24 views

Sampling Distribution of the Mean

I want to know if my reasoning is correct. Let's say I got two normal distributed variables: Variable "X": 5.4 (mean), 2.856 (variance) Variable "Y": 5.4 (mean), 5.062 (variance) Let's pick 16 ...
0
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1answer
43 views

Bivariate sampling for distribution expressed in Sklar's copula theorem?

In the univariate case, one can easily sample a distribution via random numbers $u\sim[0,1]$ and plugging into $F^{-1}(u)$. I have a bivariate distribution constructed via Sklar's theorem on Copulas: ...
1
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0answers
23 views

recovering bits from distorted signal

I have a signal: $r(t) = \sum_k a_k g( lT/2 -k(T+\Delta T) )$ where $a_k \in \lbrace\pm 1\rbrace$, $g(t)=\frac {\sin(2\pi t/T)}{2\pi t/T}$, $T/2$ is the sampling period, and $\Delta T$ is a ...
0
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0answers
28 views

Sampling combinations (from a binomial coefficient) without replacement

The total number of combinations of $k$ items out of $n$ total is $n \choose k$, or a binomial coefficient. This can be a very large number even for pretty small $n$. The binomial coefficient ...
1
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2answers
149 views

Probability of a normal random variable added to a number being greater than another normal random variable, and distribution of average

$X$= random height of a male $Y$= random height of a female $X$ and $Y$ are independent of each other For $x$, $\mu=180\text{ cm}$ and $\sigma^2= 16\text{ cm}^2$ For $y$, $\mu=170\text{ cm}$ and ...
0
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0answers
12 views

Reconstructing symbols from another set of symbols

I have a discrete-time signal as: $r_l = r(lT/2) = \sum_m h_m \alpha_{l-m}$ where $\alpha_l = \sum_k a_k g(lT/2 -k(T+\Delta T))$ where $a_k \in \lbrace\pm 1\rbrace$, $g(t)=\frac {\sin(2\pi t/T)}{2\pi ...
1
vote
1answer
61 views

Expected number of distinct nodes visited in a directed bipartite graph

Let $G = (V,E)$ be a directed bipartite graph with $V = \{I \cup O\}$ where $\left\vert{I}\right\vert = n$ and $\left\vert{O}\right\vert = m$. All the edges start from a vertex in $I$ and end on a ...
0
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0answers
23 views

Expected number of distinct nodes visited in a directed bipartite graph

Let $G = (V,E)$ be a directed bipartite graph with $V = \{I \cup O\}$ where $\left\vert{I}\right\vert = n$ and $\left\vert{O}\right\vert = m$. All the edges start from a vertex in $I$ and end on a ...
0
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0answers
24 views

Sampling from a random distribution with a margin of error

A survey of a population is taken using sampling. It is determined that 70% prefer option A and 30% prefer option B with a margin of error being 5%. Typically when simulating the process with the ...
2
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0answers
26 views

Reconstructing a signal at twice the bit-rate

I have a discrete-time signal as: $\alpha_l = \sum_k a_k g(lT/2 -k(T+\Delta T))$ where $a_k \in \lbrace\pm 1\rbrace$, $g(t)=\frac {sin(2\pi t/T)}{2\pi t/T}$, $T$ is the bit period, and $\Delta T$ is ...
1
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1answer
70 views

Distinguishing between two weighted dice (or discrete distributions)

In a bag, there are two dice, each with sides weighted differently. I know the weighting of the two dice. I reach into the bag and pick one out with equal probability. I want to know how many rolls it ...
0
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0answers
193 views

Box Muller Transform - Proving that Z is Normal Distribution

I'm studying the Box Muller transform and I cannot see how Z0 and Z1 represent standard normal distributions. I've looked at the wikipedia page for the box-muller function but they don't seem to have ...
2
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1answer
387 views

Fast fourier transform and nyquist frequency

Trying to figure out how to use Matlab to calculate the nyquist frequency of a signal. Given a function, lets say $y = 5\sin (2t + \pi /3) + \sin (t + \pi /2)$ for $t > 0$. How do we use a fft in ...
2
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1answer
22 views

Can I use one float random number to generate two random numbers, one discrete, one continuous?

I need two random numbers. The first one, u, is discrete and takes 70% of the time the value 0 and 30% of the time the value 1. The second one, v, is continuous and takes values uniformly inside [0, ...
0
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0answers
17 views

Find function of error in sampling

I was given a teaser that I can only figure out half of. Imagine there is a dartboard that is centered at (0,0). Darts are thrown and the coordinates are modeled ...
1
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0answers
25 views

Number of samples with replacement to reach expected coverage of population under non-uniform sampling

I am interested in finding the number of times $n$ I need to draw with replacement from a population of size $N$ such that the expected proportion of the population seen is at least $P$. From this ...
0
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1answer
36 views

Paths of Nearest Neighbours

I'm working on a project about sampling points, where the next point to be added to sample is the closest point to the current point. Furthermore, each point can only appear once in the sample. ...
0
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0answers
7 views

Compute mean of a set from a biased sample

I want to compute the average of an unknown set $S$ containing real numbers. I can take arbitrary large number of samples from $S$, but the samples are not uniform, meaning that some numbers are ...
0
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1answer
37 views

antithetic sampling

I am reading a book on antithetic sampling.It is said that the idea of antithetic sampling can be applied when it is possible to find transformation of $X$ that leave its measure unchanged (for ...
0
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0answers
12 views

Sample from a distribution using the log of the pdf?

I am reading about slice sampling and I understood (that as Gibbs sampling and other algorithms) you can use it when you do not know the exact pdf of the distribution, but rather a proportional ...
0
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1answer
39 views

Interpreting confidence interval of regression coefficient.

In a Simple Linear Regression analysis, independent variable is weekly income and dependent variable is weekly consumption expenditure. Here $95$% confidence interval of regression coefficient, ...
0
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2answers
56 views

Population estimate from sample

This seems very basic but I can't find a clear statement of it. Suppose I have a population of N balls which are red, white, and blue in some proportion. If I take a sample of S balls (S << N) ...
0
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0answers
11 views

Calculating average with special summary statistics

We want to compute the mean of a data set D. The data set is not accessible. Instead we repeatedly gain access to average and size of a subset of D, which contains a data point d $\in$ D and some ...
0
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0answers
8 views

Motivation for definitions of Frame, Sampling Set

In a Hilbert Space $\mathcal H$, a frame $\mathcal F=\left\{ f_n \right\}$ is a sequence of vectors that satisfy $$\forall f\in \mathcal H : A\|f\|^2\leq \sum_n | \langle f,f_i \rangle |^2 \leq B\| ...
2
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0answers
71 views

Stratified Sampling: Total and mean estimate of population

Question: In a sample survey designed to estimate the total number of cattle, the universe of 2072 farms was stratified into 5 strata on the basis of the total acreage of farms. In the hth stratum (h ...
0
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0answers
30 views

Is there a two-dimensional method to optimally allocate N sampling points on a continuous function with derivatives?

I am looking for a method to optimally allocate sampling points. I have read some papers on this topic that discuss one-dimensional allocation using chebyshev points, but I haven't found a good ...
-1
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2answers
37 views

Does the sampling distribution coincide with the population distribution if every possible sample is taken?

Say you have a population. You take random samples repeatedly, and the distribution of all the means of those random samples is the sampling distribution. Right? So does that mean, that if you take ...
0
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2answers
51 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 ...
0
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1answer
104 views

The distribution of sample proportion for given population proportion and sample size

If the population proportion is 0.90 and a sample of size 64 is taken, what is the probability that the sample proportion is more than 0.89? (4dp) work: $n=64$, $\hat p=0.89$, so $X=n \hat p ...
0
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1answer
20 views

Random sampling, need some help and guides

i was asked to do an assignment on examining the Body Mass index of students. I have to select at least 50 students from my school, and i was asked to describe how I ensure the randomness of the ...
0
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0answers
165 views

simple random sampling without replacement proof

For simple random sampling without replacement, starting with the expectation of $\sum_1^n(y_i-\bar Y)^2$, show that $V(\bar y)= (1 − f )S^2/n$ this looks very hard i tried to simplify the right ...
0
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0answers
37 views

Ergodic Versus non-Ergodic Processes

Besides time averaging not carrying over to the ensemble average (in the limit), what are the pros and cons of ergodic and non-ergodic processes? Suppose you were in an engineering situation and you ...
0
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1answer
61 views

Examining the effect of a quantitative factor on response.

To examine the effect of a quantitative factor temperature on yield,the researcher has a plan to use the following model for the analysis: $$y_{ix}=\beta_0+\beta_1 x+\epsilon_{ix}$$ where $y_{ix}$ ...
6
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2answers
204 views

How does accuracy of a survey depend on sample size and population size?

Which survey is more accurate? Assume the samples are taken perfectly randomly. A sample of 100 people out of a population of 1000 (sample is 10% of population) A sample of 1000 people out of a ...
1
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1answer
32 views

reconstruction through sinc interpolation

I have a discrete-time signal $x_k = \sum_l a_l g(kT - l(T+\Delta T))$ where $g(t) = \frac {\sin(\pi t/(T+\Delta T))}{\pi t/(T+\Delta T)}$. Since the signal $x$ has been sampled at rate $1/T>2 ...
0
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1answer
24 views

sample and population (set or collection)

In my Statistics class they introduced a population as the set of all measurements of interest to the investigator(e.g. height of humans) and a sample as a subset of the measurements selected from the ...
0
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0answers
61 views

Confidence interval of a poisson variable $\hat \lambda$ while using importance sampling to estimate $\hat \lambda$

I want to estimate $\hat \lambda$ by taking $n$ samples from a population $k$. I will sample $n$ items from population $N$ with a sample distribution $P(X)$. Therefore, my best estimate is $\hat ...
3
votes
1answer
41 views

Determine sample size according to some unknown distribution with given error rate and confidence

Assume $x\in\mathbb{N}$ obey some unknown distribution, and I can sequentially and independently acquire infinite samples of $x$. Now, given an error rate $\epsilon$ and confidence $1-\delta$, can I ...
2
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2answers
56 views

Sampling from the diamond: $|x_1|+\ldots+|x_n| \le 1$?

Let $\left(x_1, \ldots, x_n \right)$ be a point in $\mathbb R^n$. Sample uniformly at random from the diamond $$ |x_1|+\ldots+|x_n| \le 1. $$ In $\mathbb R^2$, one way is to sample the square, then ...