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-1
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0answers
9 views

completely lost. sampling distribution associated with normal populations. [on hold]

Let X1,X2, X3, X4 be a random sample of size 4 from a standard normal population. Find the sampling distribution (if possible) and moment generating function of the statistic 2X1^2+3X2^2+X3^2+4X4^4. ...
0
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0answers
7 views

Population and sample standard deviation

If the sample standard deviation of 50 sample is 2.1 then if the population is 5ooo calculate the population standard deviation.
0
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1answer
37 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 $y_{ix}$ ...
0
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0answers
43 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
vote
1answer
12 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
votes
1answer
17 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
10 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
15 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 ...
0
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0answers
24 views

How to prove this re-sampling problem

I know the following is a usual practice in the realm of re-sampling and interpolation, however, I cannot prove this: In in order to apply a constant shift to a vector/signal, we convolve it with a ...
2
votes
2answers
43 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 ...
2
votes
0answers
9 views

Is a discrete random process issued from a sampled continuous ergodic WSS process also ergodic?

I have a continuous time process $\{X_t,t\in\mathbb{R}\}$ that is WSS and ergodic for the 1st and 2nd moments. I create a random discrete process $\{Y_n,n\in\mathbb{N}\}=\{X_t,t=nT\}$ by discretizing ...
1
vote
2answers
29 views

Errors and Residual

Why are errors independent but residuals dependent? As far i know the sum of the residuals within a random sample is necessarily zero, and thus the residuals are necessarily not independent. But also ...
4
votes
1answer
58 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 ...
0
votes
1answer
47 views

Why would the discrete fourier transform “see” signals like this? What is the origin of spectral leakage?

The discrete fourier transform of $x = (x_{0},\dots,x_{N-1})$ is defined as $\displaystyle X_{k} = \sum_{n=0}^{N-1} x_{n}\omega^{kn}_{N}$ where $\omega^{kn}_{N} = e^{-2\pi ik/N}$ and ...
0
votes
0answers
5 views

Gaussian of different standard deviation and sample spacing

For given a set of samples position (e.g. $-2,-1,0,1,2$) I can define the correspondent, normalized, gaussian weights for a gaussian with std. deviation $1.0$. I know that if I scale all the sample ...
1
vote
2answers
15 views

How to pick a random sample of given size from a set of unknown size

I have the following problem: I'm reading huge amounts of data records; when done, I would like to display one or more randomly selected records from the data set. It's easy to do if I can cache the ...
1
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0answers
7 views

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 ...
1
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1answer
32 views

Computing P-value

In a book, from a sample they derived Mantel-Haenszel chi-square statistic $$\chi_1^2=1.41$$ And it is written that : this $\chi_1^2=1.41$ is associated with a one-sided P-value between $0.10$ and ...
1
vote
1answer
26 views

Estimating the mean and variance of numbers assigned to each person in population of one billion

Problem : Consider people of one billion, and each has one card containing one number. For instance first has card of number $7$. second has card of number $11$ and so on (simply if number means age ...
0
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0answers
19 views

Initializing MCMC walkers with ambiguous direction (-/+)

I'm running a sampler program where there are observations given as sample data which are derived from an equal sized population of parameters that are converted to the observations using a known ...
1
vote
1answer
40 views

Variance- covariance matrix

Consider $H$ denotes hat matrix and $e$ denotes residual. In the book Applied regression Analysis by Draper/Smith, it is written that : $\mathbb V(e_i)$ is given ...
1
vote
1answer
36 views

Confidence Interval for Regression Coefficient ,$\beta$

In the book 'Applied regression Analysis' by Draper/Smith, it is written that : Obtain individual $100(1-\alpha)\%$ confidence interval for the various parameters separately from the formula ...
0
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0answers
12 views

Covariance of independent samples

Let's say that I took a bunch of samples --may be mean age -- from a rural area in Africa and another set of samples from a very different and unrelated population in the US. Moreover, one person ...
1
vote
1answer
30 views

Random points inside a convex polytope

Given a convex polytope, defined by set of vertices $P = \{\mathbf{x}^{(i)}\}_{i = 1}^n, x^{(i)} = (x^{(i)}_1, x^{(i)}_2, \dots, x^{(i)}_d): \operatorname{conv}(P) = P$. How to generate uniformely ...
0
votes
1answer
21 views

Building histogram of latency using sample of input data

Assume I have input data set consisting of a web page response time. I'd like to build histogram from input data, but for practical reasons I can only use sample of data. Based on histogram I want to ...
1
vote
1answer
46 views

Stratified random sampling without replacement

I came across this statement and can't decide if it's true or false. Statement: In a stratified random sampling without replacement, with proportional allocation to the population size, the sample ...
2
votes
2answers
60 views

unbiased estimator in a random sample

I Have a statistic statement here which I need to decide if it's true or false Statement: "When the sample size is random, there is no way to get an unbiased estimator for the population average." ...
2
votes
4answers
135 views

Is it true that $\mathbb E[{\frac{X}{Y}]}={\frac{\mathbb E[X]}{\mathbb E[Y]}}$?

If $X$ and $Y$ are both random variables, does it hold $$\mathbb E\left[\frac{X}{Y}\right]={\frac{\mathbb E[X]}{\mathbb E[Y]}}$$ ??
0
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0answers
15 views

Spherical Sampling of Projected Disk

Given a 2D solid disk centered at some 3D point $\vec{x}$ with radius $r$ and normal $\vec{N}$, I need to compute a random unit vector from the origin that hits the disk. The vector needs to be ...
1
vote
1answer
26 views

generating random samples with a PDF

I have the PDF of a distribution from which it is not possible to get a closed from for the CDF or inverse CDF. Is there a technique that would allow me to generate samples from this distribution ...
1
vote
1answer
46 views

Non-uniform sampling of N-sphere

Suppose I have a unit $N$-sphere from which I want to draw points at random. To obtain uniformly distributed points I do the usual technique of drawing $N$ random variables $x_i$ from a Gaussian ...
0
votes
1answer
23 views

How to estimate amplitude of a sinusoid from two samples

Given a sinusoid $x(t)=A\cos(t+\theta)$, I can estimate the amplitude $A$ if I take two samples separated by $\frac{\pi}{2}$. If $X_1=x(0+\theta)$ and $X_2=x(\pi/2+\theta)$. Then, $A$ can be estimated ...
1
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1answer
22 views

Sampling on Axis-Aligned Spherical Quad

Given spherical coordinates on a unit sphere, imagine a spherical quad defined by two ranges $[\phi_0,\phi_1]$ and $[\theta_0,\theta_1]$. If you have a globe, for example, the grid formed by the ...
0
votes
1answer
20 views

Confidence Intervals and Inferences

I need help with c, as I have attempted a and b already, but believe they help with context. Suppose you took a random sample of 100 accounts in a large department-store chain, and found that the ...
1
vote
1answer
16 views

Joint Distribution and Sampling Distribution

There are three different incomes, x, and their proportions, f (x). $ 10,000 0.40 $ 30,000 0.40 $ 50,000 0.20 How do I calculate the joint distribution for X1 and X2, which are a random ...
2
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0answers
15 views

Sampling from a graph

Suppose you have a graph $G=(V,E)$ that is unobservable globally and you wish to take a sample from the vertices of that graph to infer something about its global properties from local properties. ...
0
votes
0answers
28 views

Unconditional sampling distribution of regression coefficients

I am trying to find the (unconditional) sampling distribution of a regression coefficient in a simple linear regression. The linear regression $Y = \beta_0 + X\beta_1 + \epsilon$ is conducted for $N$ ...
4
votes
2answers
101 views

To sample or not to sample?

I have the following issue (I want to predict sports results). Let $X$ be a discrete RV with $m$ possible outcomes, each having probability $p_i$, for $i=1,\ldots,m$. Assume that I have a large iid ...
0
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0answers
44 views

Trying to use Cholesky decomposition of covariance matrix to sample error ellipsoid

I'm trying to construct an error ellipsoid from a covariance matrix (which exists for a 3D point) and then sample consistent xyz points in this region. In a previous question when I asked about this ...
0
votes
1answer
81 views

Sampling error with weighted mean

I am studying statistics and I am wondering when it comes to standard error or a sampling if the calculation changes when there are weights added. I have a weighted mean: $$\mu_{w} = ...
0
votes
2answers
41 views

Why is there a difference between a population variance and a sample variance

Sorry if this answer is simple but I was wondering why is there a difference between a population variance and a sample variance? I understand The variance is calculated as: $$\text{Var} = ...
0
votes
0answers
19 views

Kalman Filter, deriving the conditional distribution for covariance matrix

I have a Kalman Filter model where: 1- State space is $x_{1:N}={(x_1,x_2,...,x_N)}$ and observation space is $y_{1:N}=(y_1,y_2,...,y_N)$ 2-$\mu_1$ and $V_1$ are the mean vector and covariance ...
-1
votes
1answer
20 views

Probability in a Random Sample [closed]

V. The mean monthly rental rate for a two-bedroom apartment in Atlanta is $\$982$ (Elle. September 1998). Assume that the population mean is $\mu = \$982$ and the population standard deviation is ...
1
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0answers
18 views

Convergence of sampling from Brownian motion

For a standard linear Brownian motion $\{B(t)\mid\ 0\le t\le 1\}$, for natural $n\ge 0$ and natural $1\le k\le 2^n$, let $d(n,k)=B\left(k2^{-n}\right)-B\left((k-1)2^{-n}\right)$ be the differences of ...
3
votes
2answers
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 $\Omega$ ...
0
votes
1answer
27 views

Consequences of violation of independence assumption in ANOVA test

Can you please explain me what is the consequences of violation of independence assumption in ANOVA test? I couldn't visualize it. Does Cochran Theorem relates to ...
0
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0answers
21 views

Pairwise independent subsets of fixed size

For a given set $\Omega$ of even size $n$, does there exists, in general, a collection of subsets $F \subset 2^\Omega$ such that $\forall A \in F. |A| = \frac{n}{2}$, $\forall \omega \in \Omega. ...
0
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0answers
6 views

“Noisy space-filling” iterator for multiple discrete finite dimensions

Suppose you have a D-dimensional space, where dimension $i$ takes values in the finite set $V_i$. Take as an example $V_1=\{1,2\},\; V_2=\{a,b\}, \; V_3=\{\alpha,\beta,\gamma\}$ One simple way to ...
1
vote
2answers
40 views

Compressive Sensing matrix

I am working with compressive sensing recovery with image and I test with various sensing matrices: Case 1: Sensing matrix A of size MxN is i.i.d Gaussian matrix. Case 2: Sensing matrix A is size of ...
0
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1answer
68 views

How to mathematically prove that we are sampling from same distributions?

The content of this question is about rigorously proving something which is otherwise considered easily correct intuitively. Let's assume we have a multivariate distribution $g(x_1,x_2,...,x_n)$ over ...