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17 views

How to do sampling for the following problem. [on hold]

There are 200 students with a mathematics exam marks. According to marks students are divided into five categories 0-20,20-40,40-60,... and I want to choose two random sample with 25 for a group. ...
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0answers
16 views

Approximation of a circle arc based on two lines, is this correct? How to rotate it afterwards?

Intro: We have two wheels that are rotated by something called T. I can tell T to rotate both wheels so much that they roll forward d cm (as shown in box A on the picture). I also have to keep track ...
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0answers
23 views

$100(1-\alpha)$% confidence interval

$100(1-\alpha)$% confidence interval for population mean $\bar Y$ $$\bar y\pm Z_{\frac{\alpha}{2}}\sqrt{\mathbb v(\bar y)}$$ Why is this $Z$ value depending on $\alpha$ important for constructing ...
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0answers
9 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 ...
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0answers
12 views

Rejection sampling multivariate case

Suppose $f$ is a complicated pdf of a random variable $X$ from which it is not easy to generate random samples. On the other hand, suppose $g$ is a pdf from which it is easy to generate random ...
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0answers
9 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
25 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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0answers
8 views

How to find sample Paths corresponding to a given co-variance function?

Given a co-variance function like $\sigma(p,k)=Cos(p.k)$ or $\sigma(p,k)=e^{\iota p.k}$, how could we find the sample paths $x(k)$ with independent random variables of mean 0 and variance 1? I need to ...
0
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1answer
19 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
34 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
27 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? ...
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0answers
5 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
22 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 ...
1
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0answers
17 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
22 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 ...
0
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0answers
24 views

Statistics, measuring unknown mean with standard deviation and probability

So I am stuck on this question and wondering if anyone can give me any hints towards it Estimate the mean pH of rainfalls in an area. Previous studies showed that the standard deviation in the area ...
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3answers
54 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
21 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
28 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
18 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
16 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 ...
0
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0answers
17 views

Oversampling and trees

I want to create a model to predict the propensity to buy a certain product. As my proportion of 1's is very low, I decided to apply oversampling (to get a 10% of 1's and a 90% of 0's). Now, I want to ...
1
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2answers
125 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
9 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 ...
0
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0answers
7 views

Sensitivity analysis of paramaters and input variables

I am trying to perform a sensitivity analysis of an optimization problem $f(x,\alpha)= \min_{ Q} {g(x,\alpha , Q)}$ where $x$ is an input variable for our function, and $\alpha $ is a parameter. ...
1
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1answer
50 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 ...
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0answers
6 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
15 views

Sampling Question about Sample Size

A random sample of $16$ has a sample mean of $400$ and a sample standard deviation of $15kg$. Assume normality. A $90\%$ confidence interval for the mean is? I got $(393.43,$ $406.57)$. ...
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0answers
17 views

Outcome of multiple samples on continuous probablity function

I'm timing a signal from it's generation to return, and trying to figure out the error due to the difference between when the signal is actually sent out / received and when the clock starts/stops, ...
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0answers
18 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
21 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 ...
0
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1answer
34 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 ...
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0answers
37 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
53 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
17 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
5 views

Difference between variance of an IID sampling distribution and the variance any sampling distribution?

If I have a population {1,2,4,4,9} and a sample size 2, the possible samples are: {1 2}, {1 4}, {1 4}, {1 9}, {2 4}, {2 4}, {2 9}, {4 4}, {4 9}, {4 9}. I understand that the mean of the sampling ...
0
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0answers
13 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
9 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
28 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
4 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
votes
1answer
25 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
7 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 ...
1
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1answer
45 views

Sin wave, sampling and plotting (Python)

I am not sure if this is the right forum for asking this question, or was it the stackoverflow, but anyway I'll go with it. So I have this python code (in a python notebook, with inlined pylab): ...
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1answer
19 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
46 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
7 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 ...
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0answers
3 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
27 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 ...
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0answers
27 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 ...
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2answers
27 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 ...