# Tagged Questions

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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### 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 $\Theta$...
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### 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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### 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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### 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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### 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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### 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 $l=1,2,3,\dots$ ...
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### 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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### 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 ...
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### 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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### 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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### 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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### 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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### 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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### 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 ...
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### 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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### 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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### 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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### 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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### 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, ...
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### 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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### 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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### 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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### 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 = ...
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### $X$ 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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### 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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### 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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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_{... 0answers 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 ... 0answers 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 ... 0answers 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 ... 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)},...
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: $N_i$; $\bar{X}_i$ ; ...