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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26 views

Probability of successful sampling fron a population

Say I have a list of 100 questions from which to study for an examination. In the examination I will be asked 10 random questions from the 100 and I pass the exam if I answer 6 questions correctly. ...
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7 views

Sampling specific unit vectors

Given a unit vector $A\in \Bbb{R}^N$ and an angle $\theta$, the unit vector $P$ needs to satisfy $\left<A,P\right>=\cos\theta$. How to sample $P$ uniformly? For example: If $A = ...
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13 views

Sampling in the time domain vs. sampling in the frequency domain

If I have a sample rate of 2 seconds on a 128 second time window (64 samples total) and then I do a Fourier transform, what is my sample "rate" in the frequency domain? Will I end up with 64 ...
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26 views

Random Variables and Statistic

I'm studying Statistical Inference by Casella and I'm confused with the definitions of random variable & statistic. So let we have the probability space $(\Omega, F, P)$ where $\Omega$ is the ...
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40 views

How sample size affects confidence interval.

Suppose the weight of n primary one students has sample mean of 20KG. If n = 40, a certain percentage of confidence interval for the population mean is (15.5,24.5). Find the confidence interval if we ...
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31 views

Comparing two populations

I have sampled from two separate populations, and I want to figure out which population is better. Population 1 has an average score of 84.1 and a standard deviation of 11.8. Population 2 has an ...
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34 views

Simulating r.v.'s from a joint density by rejection sampling in R. Continued

I wish to sample variables $v$ and $w$ from the joint density $$(v+w)e^{-\frac{(v+w)^{2}}{2x_{0}}-2\mu v-(\mu -\lambda )w},$$ where $x_0$, $\mu$ and $\lambda$ can be seen as positive constant. Since ...
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34 views

Fourier transform of a 3sinc^2(100πt)

I'm currently studying for an exam, and I'm not sure the textbook's answer for the fourier transform of 3sinc^2(60πt) is correct. For this question, I incorporated the duality property. Below is my ...
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35 views

MSE for the Method of moments estimator of variance

would appreciate some help here please - Question: Find the MSE for the MOM estimator of the variance $\hat{\sigma^{2}} = \frac{n-1}{n}S^{2}$ based on a random sample from a normal distribution. My ...
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23 views

How can I make the mean of samples be approximately equal to the mean of actual continuous signal?

Suppose there is signal f(t) that is continuous and periodic. It is known that this f is T-periodic. (but it's not necessarily a single cosine f(t).( I'd like to make the mean of samples be ...
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1answer
48 views

Probability of occurrence in a subset of a population [closed]

If 100 individuals i.e. 2% of a population totalling 5000 people, have a certain characteristic, what is the probability of two or more persons within a subset of 10 persons, taken from that same ...
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26 views

Sampling from conditional distiribution

I want to sample from condtional distribution given by formula: $$ P[T_{n+1} =t| T_n=t_n] = ...
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1answer
35 views

Chi distribution and sample variance

Suppose that the height (in cm) of randomly selected male is distributed according to normal distribution with parameters $\mu = 175$ and $\sigma = 5$. We pick a simple random sample of size ...
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28 views

Sampling from weighted sum distribution

I have $n$ probability density functions $p_1, \ldots, p_n$, which I am able to sample from. How to sample from a weighted sum of these PDFs $$c_1 p_1+ \cdots+c_n p_n$$ given that $c_1+ \cdots+c_n=1$? ...
1
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1answer
74 views

Uniform lattice sample inside a particular convex polytope

[update]: hardmath suggests using tools from linear programming. This looks like a good idea indeed. I can now tell that my feasible set is described by: $Set = \{d \in \mathbb{N}^c, -B.d\leqslant ...
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1answer
115 views

Finding the minimum sample size of an opinion poll

I have encountered the following problem in a textbook,: Assume that 28 % of voters favored party A at some point. A later opinion poll gave a result of 30 % of voters favoring party A. What is ...
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2answers
85 views

Understanding Sufficient statistic.

A sufficient statistic for a parameter is a statistic that captures all the information about a given parameter contained in the sample. My question: Is the above sentence correct. (I think it is). ...
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2answers
21 views

Checking whether the given statistic is sufficient

A random sample is drawn from a Bernoulli distribution with $X_i = 1 $ with unknown probability $p$ and zero otherwise. Examine whether the following statistics are sufficient for the parameter $p$ ? ...
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14 views

Random assignments with 95% confidence of at least $K$ duplicate assignments

I'm running an experiment online. Of my $N$ test questions, each participant sees $M$ (randomly selected, $M < N$). If I want a minimum of $K$ responses to each question, how can I calculate a ...
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28 views

Help Determining a Statistically Significant Sample Size

I am planning on conducting an advertisement test for a website. Basically, I want to know whether visitors to my website would simply just return and convert regardless of seeing an ad or not. I will ...
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0answers
19 views

Importance Sampling Distribution

I have an infinite set of events and these event are either ture or false. I perform a monte carlo simulations to find the probability of an event being true. Now I have the knowledge that $A$ % of ...
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1answer
39 views

Resampling Probability

I've had a student working on some resampling problems. Here's a question I've posed to her: M consecutive draws of size K are taken from an urn with N balls. Balls are replaced between draws. ...
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8 views

Why is importance sampling always framed as calculating E(h(x))?

In all of the tutorials I've seen, importance sampling is always framed as a way to calculate: $$E(h(x)) = \int h(x) f(x) dx \qquad x \sim f$$ I don't understand why it is not framed as a more ...
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9 views

Statistics sampling on over-lapping categories.

I got a finite population. (e.g. a pool of files) The objective of the audit is to determine whether the files are in order. I need to audit the files for 5 different category on the population. Each ...
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464 views

Sampling Distributions

Parts being manufactured at a plant are supposed to weigh 40 grams. Suppose the distribution of weights has a Normal distribution with mean 40 grams and standard deviation 2 grams. Quality control ...
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1answer
58 views

Sampling demonstration using combinatorics

Suppose that I have a finite population of A's and B's, with properties: Population size: $n$ There are $n_1$ A's and $n - n_1$ B's (so that $p = \frac{n_1}{n}$, $q = \frac{n - n_1}{n}$) I'm ...
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1answer
16 views

hypergeometric distribution and random sampling

Is there any simple and fast algorithm (to be implemented in Javascript) to obtain a sample from the hypergeometric distribution? My needed sample size is very large (100,000,000).
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93 views

Chance to pick n balls out of N numbered ones where one ball is a specific number (without replacement, order doesn't matter)

An urn contains 120 balls numbered 1 to 120. Find the probability of choosing 3 balls without replacement that includes one ball numbered “11”. My attempt: Picking "11" would have the probability ...
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2answers
57 views

Basic sampling of joint random variables

If random variables $X \in \mathcal X$ and $Y \in \mathcal Y$ are sampled jointly from a target distribution $\pi$, i.e. $(X, Y) \sim \pi(x, y)$, is $X$ sampled from the correct marginal? In other ...
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94 views

Monte Carlo sampling and Kolmogorov–Smirnov test in practice

I have two deterministic algorithms, Algorithm 1 and Algorithm 2. The first has $m$ inputs and one output, and the second has $n$ inputs and one output. The distributions of the inputs of the ...
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0answers
26 views

Sampling into two sets

Let $N$ be the set of integers $1,\cdots,n$ and let $A$ be a set of numbers sampled independently from $N$ such that each element of $N$ has probability $p=0.5$ to be selected. I am trying to answer ...
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23 views

How can I tell whether sample size is inadequate or not ?

I am given sample size of 15322 students and our research topic is to find out a relationship between students academic performance and participation in sports team. The question asks " do you think ...
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43 views

oversampling by 2, which method is correct?

I want to oversample a continuous-time signal by a factor of 2. My signal is: $ r(t_1, t_2) = \sum_i \sum_j a_{i,j} h(t_1 - iT, t_2-jT)$, where $a_{i,j} \in {\pm 1}$ and $h(t_1,t_2)$ is the kernel ...
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2answers
23 views

Can we predict next sample using the existing samples?

Suppose that I have 18 data points and I'm sampling 3 data points each time. Suppose that I have 60 samples (each has 3 data points). Can we predict the next sample (of 3 points) from the existing ...
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0answers
93 views

Importance Sampling of 2D constant piecewise function convertible to 1D?

So I have a constant piecewise 2D function (luminance values of pixels of an image) that I am writing an importance sampling algorithm for. I was going to write my algorithm by first sampling the 1D ...
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0answers
46 views

Urn with marbles, unknown number of colors

When I started with this calculation I thought this was going to be a flashback from school decades ago but now after searching I'm confused if I'm over thinking it or if it's not as trivial as I ...
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2answers
19 views

metrics for density-sampling similarity, beyond likelihood

I am looking for a metric that would evaluate the distance between a sample $S$ and a density function $D$ Building a sample from a known distribution can be done using a monte-carlo sampling, ...
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173 views

Nyquist–Shannon Sampling Theorem Counter Example?

I was learning about the Nyquist theorem regards signal processing the area of interest which I will rephrase below: Given a signal lasting infinitely long with a maximum frequency of f, then you can ...
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42 views

probability integral transformation and distribution of P= P[ |T| <= |t|] .

The task is to find the distribution of P. where , P=P[ |T| <= |t|]. (T is a continuous random variable with PDF f(t)). now , I tried to make the following two arguments : 1.P= P[ |T| <= |t|] ...
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12 views

central limit theorem and sampling dist.

If you takes samples from a distribution, and you can see that they have different variances, can the central limit theorem still be applied. The computer vision teqnique i am referring to is this ...
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1answer
37 views

Is there any known method to fit plane onto sampling data?

For example I have the variables x, y (or higher dimensional data in general) and a probability density distribution p(x,y). I want to approximate p(x,y) as a linear function, a plane in this case, at ...
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1answer
387 views

Example of a real-world situation where multivariate analysis is applicable.

I have searched a lot of site to understand the situation where multivariate analysis is applicable. But not got any easily understandable example. Would you please give me a real-world example where ...
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1answer
26 views

How to Calculate Population from A given Set Of Sampels

I have a sample set of data collected using a SRS of books with IDs from 1 to 100. {90,60,6,39,46,26,16} Using this data how can I estimate the max, in this senario I know the max id, but what if I ...
1
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1answer
66 views

Efficient method for finding the number of combinations of values so that the sum is a certain number

I know one can make a sample space for this problem, but are there any other ways of solving a problem like this: Each letter has a number value. Find all possible combinations of the letters that ...
1
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1answer
73 views

Estimate the number of trials needed to observe all the possible outcomes of an experiment [duplicate]

I am stuck with the following problem: Each package of Pokemon cards contains 1 of N possible legendary Pokemon. How many packs do you expect to buy to get all N? We assume all N legendary cards are ...
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18 views

Doubt about the degree of freedom on standard error

Once I learn that the sample variance should be $s^{2}=\sum(X_{i}-\mu)^{2}/(N-1)$, I was told that "N-1" is came from the degree of freedom, even I didn't understand well the reason. Now, I am doubt ...
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1answer
19 views

A question about importance sample and Metropolis Algorithm

I am reading this paper by Beichl, I., & Sullivan, F. (2000) on Metropolis algorithm. I understand rejection sample. In the section "The Rejection Sample", I can understand the equation: ...
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1answer
115 views

Sampling via SRSWOR and biasedness of estimates

In a survey to estimate the proportion "p" of votes that a party will poll in an election, the voter list is divided into male and female lists. A sample of 100 from each list by simple random ...
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26 views

Approximation of a circle arc based on two lines, is this correct? How to rotate it afterwards?

Intro: We have two wheels that are rotated by something called T. I can tell T to rotate both wheels so much that they roll forward d cm (as shown in box A on the picture). I also have to keep track ...
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30 views

$100(1-\alpha)$% confidence interval

$100(1-\alpha)$% confidence interval for population mean $\bar Y$ $$\bar y\pm Z_{\frac{\alpha}{2}}\sqrt{\mathbb v(\bar y)}$$ Why is this $Z$ value depending on $\alpha$ important for constructing ...