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2answers
622 views

sampling problem;

The values below are the scores (maximum 20) obtained in an aptitude test by a random sample of 11 graduates. It is known that for the non-graduate population the median score is 12. Is there ...
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1answer
15 views

Generate samples from other samples

Given a family of continuous random samples $(x_i)_{i \in I}$ that approximate some unknown probability distribution. How can I generate more samples that fit to the same unknown distibution? ...
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0answers
22 views

Antithetic pair of non-independent normal random variables

Suppose that I have two non-independent normal random variables, X and Y such that $(X,Y)$ has mean 0 and the following variance covariance matrix: \begin{bmatrix} 1 & \rho ...
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0answers
7 views

How can I calculate distribution of minima of sections of a continuous path (from a stochastic process)?

I have a long slab whose width is defined by a stochastic process, whose complete statistics I am aware of, say. I now cut it into smaller sections of uniform length, and calculate the minimum width ...
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0answers
26 views

Derivation of F distribution

Prove that the PDF of Snecdor's F distribution, given by: $$F=\frac{U/n_1}{V/n_2}$$ Where $U=\chi^2(n_1)$ and $V=\chi^2(n_2)$, is given by: ...
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0answers
11 views

filtering/detecting static regions in a given graph

I have set of points $ (x,y) $ , $x$ represent time units and $y$ represents sampled amplitude value at given frequency. $0 \leq y \leq 100$. My goal is to detect static parts of the plotted graph - ...
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1answer
8 views

Uniform sampling from part of sphere surface

I'd like to pose a question about uniform sampling on the surface of a sphere. I searched this site, and uniform sampling on a sphere surface seems to be quite a common problem. The common solution ...
4
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2answers
204 views

Monte Carlo estimator of the number of 1's in a very long binary sequence

Preface The question below is related to a problem I am working on, which requires counting the number of times a logic-valued function evaluates "TRUE" given an input value. The size of my input set ...
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2answers
29 views

Statistics - Lost with this question

I'm having trouble doing this question because I don't know where to begin. Could someone walk me through this slowly so that I understand the thought process and how to approach questions like this? ...
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1answer
31 views

Estimate correlation coefficient of unknown variable

Consider variable y depends on variable x and z linearly. I have $100$ sample values of $y$ and corresponding $x$ but don't have any values of $z$. The functional model is $$y = \alpha_1x + \alpha_2z ...
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0answers
20 views

Statistics. Sampling data $\bar{X}$

I understand that a continuity correction is required when approximating a discrete random variable by the Normal distribution and usually $+$ or $- 0.5$ is added. However when sampling and using the ...
1
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2answers
36 views

Use z confidence interval to estimate population proportion

Which of the following must be true of a sample in order for it to be appropriate to use a $z$ confidence interval to estimate the population proportion? (A) The sample is a random sample from the ...
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0answers
52 views

Asymptotic/sampling distribution

Assume we have the following function: $$f(p) = \frac{1}{(1-p)d}\ln\left(\frac{1}{T}\sum_{t=1}^{T}\left[\frac{1+X_t}{1+Y_t} \right]^{1-p} \right)$$ where $d$ is a constant $T$ is a constant $X_t$ ...
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1answer
35 views

Point estimators via method of moments

Suppose $X_1, X_2, \ldots, X_n$ constitute a random sample drawn from a population which has a probability function given by $$\Pr[X = x] = \frac{1}{\mu} \left( 1 - \frac{1}{\mu} \right)^{x-1}, \quad ...
0
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1answer
51 views

How to approximate L^1[0,1] functions?

Do functions on a uniform grid with n points in the interval $[0,1]$ approximate $L^1[0,1]$ functions, as $n \to \infty$? I want to sample functions in $L^1[0,1]$ space numerically and I want to be ...
1
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1answer
55 views

Is Sample Covariance Tied to a Specific Distribution

In many sources on data analysis, the author(s) talk about calculating covariance of the data, and the formula is given as such $$ \Sigma = cov(X) = E[(X-E[X])(X-E[X])^T]$$ This formulation is given ...
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0answers
13 views

Indepedence of sample means of two orthogonal Gaussian vectors?

Suppose $\boldsymbol{x}_{1}$ and $\boldsymbol{x}_{2}$ are Gaussian vectors with each distinct but arbitrary means and covariances, i.e., the elements of each vector are generally intra-correlated. ...
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0answers
19 views

Sampling distribution with large sample size

As the sample size $n$ of a sampling distribution of sample means increases, the distribution becomes more normal. But if $n$ were the same size as the (finite) population, the "sampling" distribution ...
1
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1answer
60 views

The radial part of a normal distribution

I am reading a paper that asks me to sample $s_i$ from a distribution like this: $s_i \sim (2\pi)^{-\frac{d}{2}}A^{-1}_{d-1}r^{d-1}e^{-\frac{r^2}{2}}$ "Here the normalization constant $A_{d−1}$ ...
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0answers
61 views

Statistics - Uniform sample vs. Representative sample

I have a question concerning two different samples, with the first being more uniform that the second. a) Chance errors are likely to be smaller... using the first set of subjects using the second ...
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2answers
62 views

Sampling Distributions: Sample size of 1 vs Sample Size of m

I saw this example from a website Suppose there is a jar containing many gumballs, each with a unique number on it. The numbers range from 0 to 32 and there is an equal number of gumballs with ...
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0answers
17 views

Correct sampling methods for this data set / requirements

I am just looking for a push in the right direction as to what kind of sampling methods I can use to fulfill this set of sampling criteria. I had thought stratified sampling, but I'm not sure if ...
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1answer
48 views

Sampling random numbers with a certain condition.

I want to randomly sample three variables that are conditioned by $$x_1 \le x_2 \le x_3$$ and $x_1\in [0,\, \ell]$, $x_2\in [0,\, \ell-\ell_1]$ and $x_3 \in [0, \,\ell-\ell_1-\ell_2]$. I have only ...
1
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1answer
96 views

calculating an incoherence property

With respect to Matrix Completion and Compressive Sampling (CS) I'm trying to understand how to calculate an incoherence property μ between two bases Φ and Ψ. Getting this incoherence is important ...
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0answers
50 views

Compressive Sensing - Incoherence Property

Compressive Sensing is built on 2 properties: 1) the sparsity of the representation basis relative to the sampling basis and 2) the incoherence between the singular vectors from each of the 2 bases in ...
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0answers
22 views

propability of largest samples of repeated random divisions

I have a bunch of numbers $A_1=\{a_{1,1},\dots,a_{n,1}\in\mathbb R^+\}=\{1,\dots,1\}$, that get multiplied by independent uniformly $[0,1]$ distributed samples, e.g. $a_{i,2}=X_ia_{i,2}$. This process ...
1
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1answer
67 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 $2k$?
0
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1answer
16 views

How do the Fourier Transform of sampling and the Frequency-domain convolution match?

The Fourier Transform(FT) is $X(\upsilon) = \int_{-\infty}^{\infty}x(t)e^{-2{\pi}i{\upsilon}t}dt$. The impulse train is $\delta_1(x)=\sum\limits_{k=-\infty}^{\infty}\delta(x-k)$, and its FT is ...
0
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1answer
49 views

Sampling without replacement

I've recently started studying statistics again, and I've just come across sampling without replacement. My book states that if we have a elements of type I and b elements of type II, then the ...
1
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1answer
69 views

Uniformly distributed points over the surface of the standard simplex

I would like to generate points that are uniformly distributed over the SURFACE of a standard $k$-simplex ($k$ dimensions, $k+1$ vertices). One way to efficiently generate points that are uniformly ...
0
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0answers
47 views

Minimum sample size to obtain population mean?

Knowing the average of a population, how could I evaluate an expected sample average based on k_sample? Data Info: Variance and standard deviation: $\sigma^2= 0.18500975256337462$ ...
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0answers
18 views

Finding properties of Inter arrival times

I apologise in advance if this is a bad question or if it's in the wrong place. Say I get a sample of inter arrival times, I'd like to have some kind of a measure which would tell me whether the ...
0
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0answers
67 views

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 ...
0
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1answer
71 views

Sets and expectations

Imagine two sets $A = \{1, 2, \dots, a\}$ and $B = \{1, 2, 3, \dots, b\}$ with $a \leq b$. Let $f$ be a uniformly independently distributed random map $f:A\rightarrow B$ and $F = \bigcup_{i=1}^a ...
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0answers
13 views

Design effect due to survey weights

I have a quick question on design effects due to survey weights. I would like to ask help since I am stuck in some particular parts though. Here it is: Show that the following expressions for design ...
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0answers
38 views

Bootstrap sampling (i.e. sample N with replacement) - distribution of histogram

In bootstrap sampling, we have $N$ items and we perform random sampling with replacement $N$ times. The resulting sample could be summarised by a histogram illustrating the number of items which were ...
0
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1answer
28 views

How can i simplify the following term to get the right side?

$$\sum_{h=1}^{L}\frac{W_h^2S_h^2}{n_h}=\frac{1}{n}\sum_{h=1}^{L}{(W_hS_h)}^2$$ where, $n_h=\frac{n}{\sum_{h=1}^{L}N_hS_h}N_hS_h$ $\quad\text{and}\quad$ $W_h=\frac{N_h}{N}$ $\quad\text{and}\quad$ ...
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0answers
132 views

Proportional random sampling from a set of variable combinations

I have this table of variables, they can have the following values: $v_1 \in \{1,2\}$, $v_2 \in \{1,2,3\}$, $v_3 \in \{1,2,3,4\}$, I need to generate all the possible combinations $v_1v_2v_3$ of ...
2
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0answers
107 views

Central Limit Theorem Clarification [duplicate]

The Central Limit Theorem states that the sampling distribution of the sample mean: Converges in distribution to a normal distribution. Has an expected value (mean of the sampling distribution of ...
1
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1answer
17 views

Deriving Statistical quantites from other quantities

Studying for a statistics exam and I am stumped on the following: For a set of sample data, the following values were found. Fill in missing values Variable: X N: ? Mean: ? SE Mean: 2.05 StDev = ...
2
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1answer
91 views

Sample size from population?

This is probably very rudimentary maths, but given a strict population size ($N = 20$ for example), is the sample size any number $<N$? For use in calculation of confidence intervals using a ...
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0answers
35 views

Variance of estimator with Importance Sampling and Resampling.

Let $p(x)$ a probability density on X, $\phi:X\to R,$ $\hat{p}$ is the normalised importance density, $\tilde{p}$ is the distribution after the resample step. I want to estimate: $E_{p(x)}(\phi).$ ...
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0answers
15 views

Gibbs sampler for local linear trend model

Question: Consider the local linear trend model given by: \begin{align*} y_t = \mu_t + \tau \varepsilon_t \ \cdots \ \text{Observation equation} \\ \mu_{t+1} = \phi \mu_t + \eta_t \ \cdots \ ...
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0answers
89 views

unbiased estimator of the area of the circle

the radius of a circle is measured with an error of measurement which is distributed normal with mean $0$ and variance $\sigma^2$,$\sigma^2$ unknown.Given $n$ independent measurements of the radius , ...
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4answers
53 views

Can a sampling based method estimate how many species exist?

I've got in to a bit of a debate online and I'm hoping some people here can help clear it up. The position I'm arguing against is "It's impossible even come up with a ballpark estimate for how many ...
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0answers
21 views

Taylor Series Expansion for Sampling Theory

There is a question which I am not particularly comfortable with doing. It is related to the Taylor Expansion for Random Variables: Let $\overline{y}_S$ and $\overline{x}_S$ be sample means, $m = ...
1
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1answer
104 views

What proportion are above x of sample size n where X ~ N(0,1) Homework

I have a homework question that I'm not quiet sure of. It follows as so: Consider a random variable $X$ that has a standard normal distribution with mean $\mu=0$ and standard deviation $\sigma=1$. ...
1
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1answer
89 views

Why Gibbs sampling needn't “remixing”

I am generating $\mathbf{x}^{(1)}, \mathbf{x}^{(2)}, \dots, \mathbf{x}^{(n)}$ using Gibbs sampling methods. So I want $\mathbf{x}^{(1)}, \mathbf{x}^{(2)}, \dots, \mathbf{x}^{(n)} \sim$ some ...
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0answers
29 views

Relation with $F$ distribution and $t$ distribution

If $X\sim F_{n,n}$ , then show that $$\frac{\sqrt n(\sqrt X-\frac{1}{\sqrt X})}{2}\sim t_n$$
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0answers
47 views

What does the hyperspace of 2d dimensions really look like?

I'm trying to follow a recipe on wikipedia (towards the end) to create some identically distributed samples from d statistical distributions: Generate an Nx2d sample matrix, i.e. each row is a ...