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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1answer
6 views

sampling and aliasing of a signal

i m given the signal x(t)=cos(100*pi*t)+cos(200*pi*t)+sin(500*pi*t) and i need to find the least sampling frequency in order to reconstruct the x(t) signal from the following of it's samples. Any ...
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0answers
21 views

why am I getting this result on a sample size calculation tool

I found an online calculator for sample size needed to perform an A/B test to a specific metric. Given a requested z-score of 1.96, a minimum detectable effect (MDE) of 5% and an estimated ...
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0answers
5 views

Sparse subgraph preserving distance for n source-destination pairs (s_i,t_i)

We are given a directed graph G with vertex set V(G)={s_1,s_2,..,s_n, t_1,t_2,..,t_n}. So G has a total of 2n vertices. Our aim is to compute sparse subgraph H of G such that distance from s_i to t_i ...
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0answers
15 views

Points in hemisphere over plane defined by a normal vector

I have the following formulas to sample points uniformly on a unit sphere in 3D space: $x = \sqrt{1-u^2} sin\phi$ $y = \sqrt{1-u^2} cos\phi$ $z = u$ where $u \in [-1,1]$ and $\phi \in [0,2\pi]$. ...
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0answers
12 views

Sampling with Clusters

Suppose we have a population of size $N$ where each individual is represented by a vector of the form, $v_i=(\lambda_1^{(i)},...,\lambda_s^{(i)})$ where $\lambda_k^{(i)}$ are finite discrete ...
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2answers
40 views

Application of power series/ binomial theorem in inverse sampling

I have posted this already in other forums. Apologies for cross posting. In order to establish some properties of inverse sampling, Haldane (1945) uses power series and the binomial theorem I ...
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0answers
89 views

Sampling a sinusoidal signal

Consider the signal $g(t)=\cos(2\pi \lambda t+\phi)$ that is sampled with a frequency $\tau$. Let $g_k$ denote the values of $g$ at the times $t_k=\frac{k}{\tau}$, $k \in \mathbb{N}$. (a) Show that ...
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2answers
31 views

What's the best guess for the parameter of an exponentially distributed sample?

I have a sample of size $N$ values. I know the values are exponentially distributed, i.e. they are distributed according to this probability density function: $$ f(x;\lambda) = \begin{cases} \lambda ...
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2answers
35 views

Probability of rejection (Sampling)

Consider a plant manufacturing chips of which 10% are expected to be defective. The chips are packed 30 to a box for distribution. A sample of size 10 is drawn without replacement from each box. If ...
2
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2answers
23 views

Probability and with replacement sampling

I'm reading the book "Model Assisted Survey Sampling" from Särndal et al. In chapter 2, there's a section about Sampling with replacement. I'll put this into context: We have $m$ independent draws, ...
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25 views

Acceptance Sampling - Random Access Memory Chips

Random access memory chips are packed in batches of $1000$. A sample of size $15$ is randomly selected from each batch and subjected to tests of reliability. The batch is accepted if the sample ...
0
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1answer
98 views

Is sharing the same support a necessary condition for exchangeability?

I am confused on the meaning of exchangeable random variables. The question is: consider the random variables $X_1,X_2,X_3$ defined one the same probability space $(\omega, \mathcal{F}, P)$; is ...
-3
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1answer
43 views

Help in probability, Difficult Question:// [closed]

Upon testing 80 resistors manufactured by a certain company, it is found that 15 resistors failed to meet the tolerance design specifications a) Construct a 92% two-sided confidence interval for ...
0
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1answer
24 views

Joint probability with housing stock data

I have a question about probability. Let’s say we have 100 homes of different ages, types and insulation levels, distributed as per the table below. Housing stock data How do I determine how many ...
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0answers
18 views

How to do non-analog sampling from a pdf

I have a distribution given by $$ f(x)=\frac{1}{2}\sinh(\sqrt{2x})e^{-x}. $$ Due to the shape of this distribution, most of my samples will be in the range $x\in(0,2]$. However, I am interested ...
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0answers
22 views

How to find sampling distribution S.D in this case

The distribution of the weights of 1000 students is normal with a mean of 55kg and a variance of 25. 100 random samples of size 16 are taken from this population. Determine the mean and standard ...
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0answers
30 views

Ways to sample a complicated PDF on an hemisphere

I want to generate samples on the upper real unit hemisphere with the following PDF (it's not really a PDF because I can't guarantee that it integrates $1$) $$\frac{\sum_{i=0}^{n}c_i(\text{ ...
2
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1answer
61 views

sampling distribution question

Need clarification on a binomial sample example: we drew a sample of size $100$ from a binomial($m = 2$,$p = 0.2$) distribution and observed $76$ of the $x_i = 0$, $20$ of the $x_i = 1$ and $4$ of ...
1
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1answer
24 views

compute probability density function of a bivariate function without sampling

Suppose $X_1 \sim f_{X_1}(x_1)$, $X_2 \sim f_{X_2}(x_2)$ are random variables with known probability density function. Is there any way to compute the probability density function of a bivariate ...
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2answers
22 views

Simulation methods and generating random variables

Twenty aircraft are sent to bomb a target that is rectangular in shape. It has dimensions 150m by 50m. Each aircraft makes a bombing run along the horizontal x axis and drops one bomb. The point ...
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0answers
21 views

How Much of a Distribution has One Seen After N Samples with Replacement?

I frequently run into this question while modeling processes. I am wondering if there is a general solution or approximation. The question I run into is: For a given distribution with a finite ...
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0answers
11 views

upsampling and plotting a signal in matlab

I want to upsample by 5 a signal in frequency domain, and then plot(stem) it. I figured how to upsample, Fk=(1/5)*upsample(ak_new,5) now this creates a vector ...
1
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1answer
31 views

Basic questions concerning sample means and distributions

I have the following questions: Is The value of the sample mean always the population mean $\mu$, in any sample? I am confused about whether or not it is. Is the sampling distribution of the sample ...
1
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1answer
17 views

hemisphere sampling and vector flip

I am currently implementing a uniform sampling of a hemisphere. Since my hemisphere is oriented around a specific vector N, whatever the sampling algorithm used (uniform/cosine ...
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0answers
27 views

Bound expected sample mean error

Given $n$ numbers $x_1, \cdots, x_n\in [a,b]$, randomly sample $m$ numbers without replacement $x_{i_1}, \cdots, x_{i_m}$. How can I bound the expectation $$E_{i_1, \cdots, ...
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0answers
20 views

Variance of Importance Weights in Importance Sampling

What is the variance of importance weights in Importance Sampling? Is it good to reduce the variance of importance weights and why? And what is the optimum proposal in importance sampling? I assume ...
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0answers
53 views

Drawing successive related samples from a Gaussian distribution

I have a question which describes a system where successive samples are drawn from a Gaussian distribution, and each sample is defined with the following relation. $v_{k+1} = \gamma v_k + \eta_k$ ...
0
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0answers
19 views

How to do importance sampling if $ f(x)=\frac{\sin x}{\ln x}$?

Let $$ f(x)=\frac{\sin x}{\ln x }$$ In importance sampling, I should choose $g(x)$ to reduce variance. My question is, what kind of function should I choose if $f(x)=\frac{\sin x}{\ln x}$ (like ...
0
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2answers
43 views

$\cos(2\pi f nT +2\pi N_n) =\ cos(2\pi f nT)$ and more, why?

I am studying signals and systems and this came up? Could someone explain why is $\cos(2\pi f nT +2\pi N_n)$ equal to $\ cos(2\pi f nT)$? The book says: "because $N_n$ is an integer" I am ...
1
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0answers
18 views

Drawing uniform samples from the *range* of a non-invertible function

I am looking for a Bayesian technique to draw samples from a uniform distribution over the range of a non-invertible (that is, there isn’t even a formula) function $\mathbf{f}: \mathbb{R}^N ...
0
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1answer
26 views

Fourier transform of sampling function

Calculate the Fourier transform of $f_{ZOH}$ (the zero-order hold reconstruction of a sampled signal). Where $f_{ZOH} (t)= f(kT), \ \ kT \leq t < (k+1)T,$ and the sampled signal is $$f_s = f(t) ...
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0answers
14 views

Getting a feel for the Normal-Inverse-Wishart conjugate prior to multivariate normal distribution

I am trying to get a feel for the Normal-Inverse-Wishart conjugate prior, which I have started to use, sparingly, in my work, where I am trying to cluster multivariate normal data. As Wikipedia ...
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0answers
22 views

Sampling from Irwin-Hall (Uniform Sum) distribution using rejection sampling

Irwin-Hall Distribution is a probability distribution for a random variable defined as the sum of a number of independent random variables,each having a uniform distribution True or False: The ...
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0answers
9 views

Sampling from Irwin-Hall distribution using triangular distribution

So I need to sample from the Irwin-Hall distribution using rejection sampling with the triangular distribution. I built 2 functions: The first is d_irwin which receives an $x\in supp(g)$ and the n we ...
1
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0answers
28 views

Generating continuous random variables from a set of Bernoullis

Given a set of $Bernoulli(p_i)$ variables with each having its own arbitrary $p_i$, is there an efficient way to generate continuous random variables sampled from an arbitrary distriubution? To ...
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0answers
15 views

Intuition behind sampling distributions – specific case

I'm still trying to understand the basics of understanding the intuition of sampling distributions and calculating the sampling distributions of common estimators. For example, I understand the ...
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0answers
22 views

How to approximate a probability distribution vector by sampling

Given a probability distribution vector $\overrightarrow{p}=(p_1,p_2,\cdots,p_n)$ (of course $\sum_{i}^n p_i=1$), assuming we can sample the distribution with obtaining $i$ with probability $p_i$, how ...
1
vote
1answer
55 views

How to choose new points after grouping/resampling?

I'm resampling a signal (which takes values [0,1]) of N samples (blu points) to one with N/5 samples, where (for each group of 5 samples) I store in two arrays the max and the min values of the ...
0
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2answers
37 views

Probability of inequalities between max values of samples from two different distributions

Given samples from two empirical distributions (not necessarily passing tests of normality, but a solution for the normal case would definitely be useful) what's the probability that the maximum value ...
0
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1answer
23 views

Do 'Sample from' and 'insert parameter' commute?

The Setting is as follows: We are given random variables $X$ and $\Theta$ but we are not so much interested into $X$ itself as its Distribution needs a Parameter $\theta$ which is produced by ...
2
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1answer
42 views

Equation for estimation of sample size is a quadratic?

The equation for calculation of sample size for a prevalence study happens to be $$\ n= \frac {Z p (1-p)}{e^2}$$ where $Z$ is the $Z$ score, $e$ is the precision we want to achieve and $p$ is the ...
2
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1answer
32 views

Mod of a random variable

I had this problem where I wanted to generate random variables (discrete) in a way that certain numbers were more probably than others (basically geometric) but since I wanted to use this number as an ...
1
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1answer
37 views

Vertex and barycentric coordinate enumeration for a polytope

Problem 1 Enumerate all the vertices of the polytope defined by: ${\bf Ax}\leq {\bf b}$ where ${\bf A} \in R^{m \times n}$, ${\bf x} \in R^n$, ${\bf b} \in R^m$ and each element of ${\bf x} = ...
0
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2answers
26 views

Do unbiased estimators have to be exactly equal to the true value of the parameter?

Is it true that for an unbiased estimator, the mean of the sampling distribution is very close to, but not always equal to, the true value of the parameter being estimated? My textbook says that "An ...
6
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1answer
3k views

Probability to choose specific item in a “weighted sampling without replacement” experiment

Given $n$ items with weight $w_n$ each -- what is the probability that item $i$ is chosen in a $k$-out-of-$n$ "weighted random sampling without replacement" experiment? Can a closed-form solution that ...
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0answers
23 views

Multivariate Inverse Transformation Sampling

Summary Given a multivariate density distribution, I use inverse transformation sampling to sample points from this distribution. While the first dimension exhibits the correct distribution, all ...
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0answers
24 views

Padua points or Chebyshev grid for more than two dimensions?

I'm looking for a good point grid in order to sample from a (polynomial) function $f:R^n\rightarrow R$ at discrete points lying in a rectangle. I don't need any weights or interpolating polynomial. I ...
0
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0answers
26 views

Compare two samples tests

Sampling $1000$ birds from a population which has $10$ types of birds the expected outcome is $100$ birds of each type (this is for the sake of simplicity; general case is each distributed with ...
2
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1answer
82 views

Correlation between probability of events

Suppose there are two events $A$ and $B$ and that $P(A|A\cup B)P(B|A\cup B) = P(A\cap B | A \cup B)$. Then I am asked to find if $A$ and $B$ are independent, positively or negatively correlated. My ...
3
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2answers
44 views

Determine periodicity from transition matrix?

I have a two part question. Let's say we have a transition matrix T: \begin{bmatrix} 0 & 0.2 & 0.8 & 0 & 0 \\ 0.7 & 0 & 0.3 & 0 & 0 \\ 0.6 & 0.4 ...