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2
votes
1answer
10 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, ...
-2
votes
0answers
22 views

Nyquest rate is given, what is the bit rate? [on hold]

$$A=8\sin(\omega t+\theta)$$ is sampled at Nyquest rate. What is the bit rate of sampled signal?
0
votes
0answers
4 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
votes
0answers
12 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
vote
0answers
8 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
votes
1answer
22 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
votes
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
23 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
votes
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
vote
1answer
25 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): ...
0
votes
1answer
14 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
votes
2answers
41 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
votes
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 ...
0
votes
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
votes
0answers
21 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
votes
0answers
26 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
votes
2answers
25 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
votes
0answers
19 views

Largest hole in uniform sampling of $m$-torus

Let $M$ be the flat m-dimensional torus $(\mathbb R/\mathbb Z)^m$ with the standard Riemannian metric. I would like to know the probability that, given a uniform sampling $X$ of size $N$, there is a ...
0
votes
2answers
40 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
votes
1answer
33 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
votes
1answer
16 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
votes
0answers
37 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
votes
0answers
15 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
votes
0answers
11 views

Population and sample standard deviation [closed]

If the sample standard deviation of 50 sample is 2.1 then if the population is 5ooo calculate the population standard deviation.
0
votes
1answer
48 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
votes
0answers
47 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
15 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
21 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
votes
0answers
19 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
21 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
votes
0answers
25 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
48 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
12 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
40 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
71 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
54 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
6 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
18 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 ...
2
votes
0answers
10 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
vote
1answer
35 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
votes
0answers
20 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
46 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
48 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
votes
0answers
15 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
36 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
27 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
60 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
68 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
137 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 $$\mathbb E\left[\frac{X}{Y}\right]={\frac{\mathbb E[X]}{\mathbb E[Y]}}$$ ??