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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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 $\Theta$...
2
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1answer
42 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 ...
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2answers
33 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 ...
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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} = \{x_1,...
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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 ...
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0answers
36 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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27 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 ...
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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
44 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
84 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 ...
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2answers
49 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 &...
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1answer
34 views

Statistically quantifying a variable with a limited number of samples

Regarding a variable which at any time can have one of two values, but which we only have a limited number of samples for, I'd like to be able to make a statement along the lines of: With 95% ...
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34 views

Sample size for 95% Confidence

If $X_i$ and $Y_j$ are normal distributions where $i = 1,...,n$ and $j= 1,...,n$ with different $\mu$ but same $\sigma^2$, and $\mu_x$ - $\mu_y$ = $\sigma/3$ what is common sample size $n$ needed to ...
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0answers
12 views

Determine two sets of samples being independent by fisher exact test method

I am using Matlab to determine two sets of samples being independent by fisher exact test method. Now I have generated 1000 samples for both random variables, and I already used reject-accept sampling ...
1
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1answer
24 views

Sampling Without Replacement : Draw x Red before Drawing RGB

I am struggling to get my head around how to solve the following problem and can only find solutions to simpler versions Consider a bag containing x Red, y Blue and z Green marbles What is the ...
0
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1answer
26 views

sampling distribution of mean

Suppose we have a binomial population with parameters $n$ and $p$ so that the mean in $np$. How to find the sampling distribution of mean from the population?
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11 views

How does a DTFT relate to physical frequency?

After performing a DTFT and normalizing the frequency plot I ended up with the following figure The resulting data is correct, as the input signals were of 5kHz and 25kHz frequency. The part I am ...
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1answer
24 views

Sample variance: degree of freedom argument

In sample variance we divide by n-1 and not n. I know a couple of arguments for this - one is that this is sort of a normalization to ensure that the expected value of sample variance is equal to ...
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0answers
11 views

U-statistics and Independent Sum

I have i.i.d. paired samples (X,Y): $(X_1, Y_1), (X_2, Y_2), \dots, (X_n, Y_n)$ I compute the statistics $\sum_{i \neq j} X_i \cdot Y_j$ People have told me that the above is actually a sum of $n$ ...
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0answers
17 views

p-value of probability distribution

Suppose $\{X_{i}\}_{i=1}^{50}$ are independent and identically distributed samples from the following probability distribution: $$(1/\theta)\exp(-x/\theta); \hspace{1mm} x>0.$$ Given $\sum_{i=1}^...
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1answer
44 views

Find the mean and standard deviation of the sampling distribution of the restaurants sample mean expense per customer.

A restaurant charges $8.95$ pp. Management finds it's expenses per person has a distribution that is skewed to the right with a mean of $8.20$ and a standard deviation of $3.00$. Q: If $100$ ...
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12 views

The exact usage of Sequential Monte Carlo for distributions over time?

I have wondered the usage of Sequential Monte Carlos and it is used as an alternative to Kalman filter for example. However I wonder if this can be also used for simulating a distribution over time? ...
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1answer
58 views

Wanted: Polynomial $P(x)$ with $P(-l(l+1))=1/(2l+1)$, for $l\in \mathbb{N}$

I'm looking for a polynomial $P(x)=a_1+a_3 x+ a_5 x^2+\dots$ (numbering of $i$ in $a_i$ is due to the application of this) with sampling points $P(-l(l+1))=\frac 1{2l+1}$, for $l=1,2,3,\dots$ ...
2
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0answers
64 views

Sampling from a given pdf

I have the following pdf: $$ f(x) = C x^d I_0\left(b \sqrt{- \log\left(\frac{x}{A}\right)}\right)$$ for $0 < x \leq A$, $C$ is a normalizing constant, $b$, $d$ are constants, and $I_0$ is the ...
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1answer
19 views

Simple Random Sample

Suppose a company has 500 employees and wishes to select a simple random sample of 25. Which would be the more appropriate way of doing so? Choose 25 pages of the employee directory, and take the ...
1
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1answer
31 views

Probability that a sample represents between X% and Y% of the population

Really no idea how to go about this. I thought about using a uniform normal distribution law but the answers I got made no sense. In a country that has a population between 1500000 and 3000000 people,...
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32 views

How to estimate a distribution from samples in a histogram

Given a r.v. $\tau$ , I've computed $\Bbb{P}(\tau >a)=e^{-Nx}(e^{Nxe^{-a}}-1) $ , where $N\in\Bbb{N}_{>1} $ and $ x\in \Bbb{R}_{>0} $ are just fixed parameters; say $N = 2 $ and $ x = 1$, ...
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0answers
15 views

Arithmetic of sampling

INTRO: Suppose that a large set $Z$ is divided to two subsets $Z^A$ and $Z^B$, such that each element of $Z$ has a probability of 1/2 to be in each subset, independently of the others. By the law of ...
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2answers
28 views

What does one sample average tell me about the average of other samples?

I'm sure this has been asked before but I can't find the exact variant I'm looking for. I have an infinite population of elements. I take a sample of those, say 10000, and make a measurement for ...
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69 views

subsample order statistics

I am interested in characteristics depending of the $r$-th order statistics $X_r$ of a distribution with unknown pdf. For example, I would like to estimate the Gini mean difference $E(|X_r - X_r'|)$, ...
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1answer
34 views

How to test a collection of samples are sampled with replacement or not?

A box is full of balls with $m$ different colors, and for each color, there are $n$ balls. So the total number of balls is $m*n$. Note that $m$ is unknown, $n$ is already known, and balls can only be ...
1
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1answer
27 views

Finding the probability of X_Bar with sample variance included?

The question I am asked is $P(\bar{X} > 3 + 0.4984S)$, where I am additionally provided $n = 25, \mu = 3.0, \sigma^2_\text{pop} = 3.0$. $\bar{X}$ is the sample mean and $S$ is the sample variance. ...
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47 views

Signal processing and algebraic geometry

Signal processing is a pretty huge branch of what I would (maybe wrongly) call electrical engineering. I have heard here and there whispers of interesting connections between signal processing - in ...
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1answer
20 views

comparing probability of different size

I have a set of items. Each item has a probability of correctness calculated from no. of correct/no. of attempts. For example item A has 100% of being correct out of the 10 attempts he did. On the ...
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30 views

Choosing a threshold for the population by using a sample

Can someone please give me some insight about this problem I have come across. Say I have a population "N" for which I want to figure out a threshold "T" of a score(the score can be for anything for ...
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8 views

How should I set the weights on a linear calibration to make more recent values matter more?

I have a program that interpolates raw values to real values using a linear regression. The linear regression function takes three arrays, X, ...
1
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1answer
36 views

How many 'zero' elements in $\mathrm{A}+\mathrm{B}$ after randomly letting one entry in $\mathrm{A, B}$ be $0$ for $m$ times,respectively?

Both $\mathrm{A}$ and $\mathrm{B}$ are $d$-dimensional vector with all the elements being $1$. Then we randomly and uniformly pick one element from $\mathrm{A}$ with replacement, and let it be $0$. We ...
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1answer
31 views

Can random sampling affect view of how much repetition there is in a data set?

$X$ unique individuals take $Y$ actions. If I sample $1\%$ of the actions entirely at random what is the relationship between the number of unique individuals seen in my sample and $X?$ (In my ...
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39 views

Small Sample size Confidence Intervals

Health insurers and the federal government are both putting pressure on hospitals to shorten the average length of stay (LOS) of their patients. The average LOS for men in the US is 5.2 days and the ...
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2answers
61 views

Two-sided confidence intervals and tests

From a sample of 1751 army hospitals, estimate the mean expenses for a full time equivalent employee for all US army hospitals using a 90% confidence interval given x = ...
1
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1answer
29 views

$X$ is exponentially distributed $\varepsilon(\theta)$. Using the Method of Maximum likelihood find the best (marking?)Question its centeredness

$X$ is exponentially distributed $\varepsilon(\theta)$. Using the Method of Maximum likelihood find the best (marking?)of sample $n$ for parameter $\theta$ .Question its centeredness and existence. ...
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0answers
58 views

Intuition behind rejection sampling proof

I have a quick question about the proof of rejection sampling. Suppose we know how to sample from a distribution with $Y$ pdf $q$, and want to sample from a distribution $X$ with (known) pdf $\pi$. ...
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0answers
34 views

Uniform Sampling & CDF inverse

I have a probability exam soon, and our prof told us to study the following question: "Describe a procedure for generating independent identically distributed (i.i.d.) samples of a random variable ...
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1answer
57 views

Expectation and variance without replacement

Let $X_{N_1},\cdots,X_{N_n}$ is a sample without replacement from the set $\{1,2,\cdots,N\}$, and let $\bar X_n=\sum_{i=1}^n X_{N_{i}}/n$. Then, how one can find $E(\bar X_n)$, $Var(\bar X_n)$, $\max_{...
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30 views

Question about confidence intervals

I have questions regarding the calculations and computations of confidence intervals basing upon the given accuracy. Here is the description from the textbook: The public health authority wants to ...
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19 views

sample size calculation for count data

I have a plan to see some treatment effect in several projects in my company where I will compare the average number of errors now and after the treatment. So what I know from current situation is ...
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51 views

A Question dealing with Surveys

I did the following problem but I do not have confidence that I did it right. Could somebody please check it for me? Thanks Bob Problem: In an organization of $1000$ employees, a survey was made ...
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0answers
16 views

Sampling sequences of random vaiables without replacement in a weighted fashion

Let's we say have $n$ random variables $x_1,x_2,\dots,x_n$. Assume for any random variable $x_i$ the set of all possible outcomes is $\left \{a,b,c,d\right\} $with probabilities $p_1^{(i)},p_2^{(i)},...
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27 views

Cluster sampling: Compare efficiencies

A company operates from 12 branches, and the numbers of cars, $N_i$ and means $\bar{X}_i$ and variances $S_i^2$ of miles driven last year for each brand, are as follows Branch: $N_i$; $\bar{X}_i$ ; ...
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29 views

Simple Random Sampling: Find the variance

I have trouble answering this simple question. There is a total of 280 trees. The assessed total yield is at 432,6 tons. 25 trees are picked at random and their timber yields are accurately ...