Stack Exchange Network

Stack Exchange network consists of 174 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [sampling]

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.

0
votes
0answers
13 views

Statistics - Question on Sampling

Here's the question The scores, $X_1$ and $X_2$, in papers $1$ and $2$ of an examination are normally distributed with means $24.3$ and $31.2$ respectively and standard deviations $3.5$ and $3.1$ ...
0
votes
0answers
24 views

The relationship between sample and population skewness [on hold]

Get the sample skewness coefficient of a random variable X from a random sample of size n. Explain why it measures asymmetry of the distribution of X. Explain the relation between the sample skewness ...
1
vote
1answer
11 views

Compute mean and covariance matrix of $\bar{X}$ from a simple random sample

Given $\{X_\alpha , \alpha =1,...N\}$ a simple random sample obtained from any p-dimensional distribution with mean $\mu$ and covariance matrix $\Sigma$, compute the mean and the covariance matrix of $...
1
vote
0answers
22 views

How to continue sampling after a conditional rejection?

I encountered the following (to me) weird problem while trying to do some simple sampling. I have a system that generates random numbers. Let's for simplicity assume the numbers are 0, 1 and 2 with ...
0
votes
0answers
10 views

Sample from Poisson process with no collisions.

On a 2D square $[0,\ 1]^2$, I can draw a random configuration of points $c = (n,\ (x_i)_{1..n})$ with interesting independence properties using a Poisson point process: draw the number of points $n \...
0
votes
1answer
22 views

Comparing two random variables with monte carlo sampling

Suppose there are two numbers X1 and X2 that are from a random continuous probability distribution with unknown range. You are given the value of X1 and you need to determine whether X1 is less than ...
0
votes
0answers
19 views

Constructing an upper confidence limit for $σ^2$

Suppose that $X_1, ..., X_n$ form a random sample from the normal distribution with unknown mean µ and unknown standard deviation σ. Construct an upper confidence limit U(X1, ..., Xn) for $σ^2$ such ...
1
vote
1answer
76 views

Problem of statistical inference Poisson

I am having problems solving this problem of statistical inference and I do not know if it is well done or not, so I would like someone to review it. I just started with inference, so I have my ...
0
votes
1answer
17 views

Using Random Sample to Find Estimate

I have to use the Inversion Sampling Method to generate a random sample of 100 from the function $f(x)=\theta x^{\theta - 1}$ if $\theta =5$. Here is my function so far: ...
0
votes
1answer
20 views

Showing that an estimator is consistent

Let $X_1,X_2,\ldots,X_n$ be a random sample from $\mathcal{N}(\theta,1)$. Consider the following (randomized) estimator of $\theta$ given a sample of size $n$: $$ \hat{\theta}_n = \bar{X} + \begin{...
0
votes
2answers
19 views

Finding the Expected value of $\hat{\theta}_n$

Let $X_1,X_2,\ldots,X_n$ be a random sample from $\mathcal{N}(\theta,1)$. Consider the following (randomized) estimator of $\theta$ given a sample of size $n$: $$ \hat{\theta}_n = \bar{X} + \begin{...
0
votes
0answers
15 views

Showing that a estimator is consistent

Let $X_1,X_2,\ldots,X_n$ be a random sample from $\mathcal{N}(\theta,1)$. Consider the following (randomized) estimator of $\theta$ given a sample of size $n$: $$ \hat{\theta}_n = \bar{X} + \begin{...
0
votes
0answers
21 views

How to show that $\sum_{i=1}^m (X_i−X_m)^2$ and $\sum_{i=1}^n(Y_i− Y_n)^2$ are independent

Let $X_1,...,X_m$ be i.i.d. sample with $N(\mu_1,\sigma^2)$, and $Y_1,...,Y_n$ be i.i.d. sample with $N(\mu_2,2\sigma^2)$. Let $S_x^2 = \sum_{i=1}^m (X_i−X_m)^2$ and $S_y^2= \sum_{i=1}^n(Y_i− Y_n)^2$...
0
votes
1answer
21 views

Using normal distribution to calculate $P(52.1 < \bar{x} < 53.9)$

I am given the following question in one of the lectures I was looking through. Suppose a random sample of size $n = 400$ is to be selected from a population of size $N = 2000$. A quantitative ...
0
votes
0answers
20 views

Is MCMC (or any sampling for that matter) explainable?

Recently, at an interview, I was asked if you use MCMC to build Maximum a posteriori (MAP), and use it for an inference, will the system you create have an explainability? Now, explainability is ...
-1
votes
0answers
15 views

Sampling distribution - approximately normal?

If the population distribution is skewed to the left, the mean is 25,000 and the standard deviation is 2,500 and the randomly selected n=100, would the sampling distribution of the sample mean be ...
1
vote
2answers
209 views

Confusing Sampling from observed data

Suppose we are given some small set of data on bundles of electrical wires and increasing voltages run through them, and we note how many of the individual wires fail. So for example, a large data ...
0
votes
0answers
11 views

Sampling a conditional joint distribution of continuous random variables using samples from joint distribution and marginal distributions

I am seeking an approach to sampling conditional joint distribution (new to probability). I will put my case in a simple way: Similar question for discrete variables is asked here but not yet ...
0
votes
1answer
18 views

Sample calculation

I have knowledge about the calculating sample, but i am unable to solve this question for the last two hours. Please check this question. A bank believes that approximately 2/5 of its checking-...
0
votes
0answers
15 views

The mean value of sample moment with order k

I've this problem of statistics that I can't resolve. So I hope that someone can halp me. The problem is this: Let sampling moments $\overline{X_n^k}=\frac{1}{n}\sum_{i=1}^nX_i^k$, where for $k=1$ $...
1
vote
1answer
33 views

Determining sample size given true proportion.

I'm attempting to solve a problem from a statistics course in regards to finding the sample size I need to take when given the Margin of Error, Confidence interval, and 'true proportion' (probability)....
0
votes
0answers
28 views

Working out expectation of a random sample.

I have the problem: Let $X_1, X_2, X_3, X_4$ be a random sample from a population that has mean $μ$ and variance $σ^2$. Find $\mathbb E[(X_1-X_2)^2]$ and hence the value of $k$ such that $T ...
1
vote
2answers
23 views

What is the probability that $m$ items drawn from $n$ distinct items contain all $n$ items?

Suppose there are $n$ distinct items to be drawn with replacement for $m$ times, the probability of each item being drawn is assumed to be $\frac{1}{n}$. What is the probability $P(m)$ that $m$ items ...
0
votes
0answers
9 views

Sampling from joint discrete distribution

I have a set of items $a_1, a_2, \dots, a_n$. My aim is to generate from this set of items, a list of item tuples $\{(a_i, a_j), \dots\}$ such that $a_i\ne a_j$. The constraints are as follows. The ...
0
votes
0answers
13 views

Sampling binary values from a discrete probability distribution

Suppose that we have a discrete non-uniform probability distribution X over $\{0,1\}^k$ for n binary noise values. Let $e = (e_1 ,..., e_m)$ be a vector of independant identically distributed binary ...
0
votes
1answer
17 views

Prove the sampling distribution of $S^2$ has the mean $\sigma^2$ and the variance $2\sigma^4/(n-1)$

I would like to ask whether anyone would mind providing me with some direction on how to proceed with this proof. The question asked me to use the theorem below to prove that, for random sample of ...
1
vote
0answers
22 views

calculating variance and expectation of unknown binomial variables over a window

I have $2^m$ independent random variables. All have binomial distributions, each with $m$ samples. The probability of success for each binomial distribution is somewhere in the range $[0,p]$ (...
0
votes
2answers
28 views

Definition of sample mean

I've seen two definitions of sample mean on the internet. One definition defines it as the average of Random variable other defines it as the average of sample values of a sample. I'm confused which ...
0
votes
0answers
11 views

Taking the expectation of gaps from uniformly chosen points

Suppose I choose $k$ points $x_1, \dotsc, x_k \in \mathbb{R}$ independently with distribution $D$. I'm interested in the value (or an approximation) $$ \mathbb{E} \left( \operatorname{max}\limits_{i=...
0
votes
0answers
19 views

Sample new point from set of points

I need guidance to solve the following problem, I'm only looking for directions to follow Given a set of points $X$ laying on an $n$ dimensional surface with an unknown density. The aim is to sample ...
0
votes
0answers
12 views

Trying to understand the meaning of Average outgoing quality

I was following an example in my stat's book that had the following information. Find the AOQ given $N=2000, n=50$, and $c=2$ With a $2\%$ nonconforming. I calculated the $P_a=0.920$, and using the ...
0
votes
0answers
19 views

sampling from an existing sample

I have an existing data set with 8 000 observations. I want to check an association between two parameters in the data set. I also want to see if maybe for this purpose I do not need 8 000 ...
0
votes
0answers
18 views

Setting weightage for random sampling to ensure the sample has a certain distribution

I have 165 red, 239 blue and 495 green balls, making a total of 899 balls. I need to pick 150 balls from these through weighted sampling without replacement. In the end I want to have picked approx. ...
0
votes
1answer
27 views

Proof/Explanation of Dependence of Two Random Variables (Drawing Cards with Replacement)

"Two Cards are picked from a deck with replacement. Let X= number of aces, and Y= number of kings. X and Y are both discrete random variables that can take on 0,1 and 2." I'm trying to show whether ...
1
vote
0answers
24 views

Sampling Distribution of samples drawn from an arbitrary (non uniform) probability distribution

I am quite new in the probabilistics field, and I am trying to figure out how would drawing n samples from a probability distribution perform. Suppose We have a non-uniform probability distribution D ...
0
votes
0answers
11 views

How to prove Gradient-based One-Side Sampling in LightGBM

https://papers.nips.cc/paper/6907-lightgbm-a-highly-efficient-gradient-boosting-decision-tree.pdf In LightGBM article, how to prove the Theorem3.2?
1
vote
1answer
12 views

How do I uniformly sample from sorted combinations

I'd like to sample a random sorted combination with replacement. (Ideally I'd like to do this without rejection, or otherwise in a computationally-efficient manner) I can start by sampling a ...
0
votes
0answers
20 views

Size-biased sampling for family size

Imagine taking a survey of the average family size in a certain neighborhood. One way to achieve this is to survey a random sample of women to ask how many children they bore. Let $N$ be the number of ...
3
votes
3answers
75 views

Does a data-dependent sampling rule induce correlation?

I'm struggling to understand whether a data stream sliced up in a certain way could produce two quantities that are dependent but uncorrelated. Suppose I have two iid streams of data that are ...
0
votes
0answers
18 views

Estimate the number of elements in a ordered set less than x

Suppose U is an ordered set, S⊆U, and x∈U, estimate the number of elements in S ≤ x; Is there a way to sample the S and maintain a structure whose size ≤ log(|S|) from which for any x ...
2
votes
0answers
24 views

How to randomly sample a social graph to find paths between at least 20% of profiles?

Given a Graph, where we know Total number of nodes (~100,000) Average no of connections per node (~200) Maximum distance between two nodes (~5) How many nodes (and its connections) do we have to ...
0
votes
0answers
19 views

How to find a proper bivariate Gaussian distribution that integrals 95% over a convex polygon

I have a known 2-D convex polygon, and my goal is to find a bivariate Gaussian distribution, that 1) samples from the Gaussian falls into the polygon 95% of the times, and 2) should be reasonably ...
1
vote
0answers
39 views

How to distribute N approximately equispaced points with a given probability density?

Let $x_i$ be points in $R^D$ space, $i = 0\ ..\ N-1$, where $N$ is fixed. The problem is to distribute the $N$ points in the space so that their density is equal to given probability density $p(x)$, ...
1
vote
0answers
44 views

Is there a more efficient expected value estimator than the sample average?

I'm wondering if there is a known estimator for expected value that is more efficient than the sample average. If that is not the case for an arbitrary random variable, then maybe there are examples ...
0
votes
2answers
91 views

Sampling from a continuous distribution

The Lebesgue integral of the standard normal pdf over $\mathbb{Q}$ is equal to zero, since the rationals are countable and thus have measure zero. So the probability of "drawing" a rational number ...
2
votes
1answer
37 views

Probabilistic subsampling of an Erdős–Rényi graph

Suppose I have an Erdős–Rényi graph ${\cal G}(n,p)$, where $n$ is the total number of nodes and $p$ is the probability of an edge between any pair of nodes (edges are added independently). I subsample ...
3
votes
1answer
76 views

Proving $E(\hat s^2)=V(\bar x)$ for finite population

Population is $X_1,X_2,...,X_N$ with large but finite $N$. Sampling indicator $Z_i \in(0,1)~ \forall i$ , such that $\sum^N _{i=1}Z_i=n$ and $Pr(Z_i=1)=\frac {n}{N}$. Sample mean in this case is $\...
1
vote
0answers
21 views

Sampling extreme points from Minkowski Sum

I recently stumbled upon the following subproblem: we are given zonotopes $P_1, \dots, P_m$ in $\mathcal{V}$ representation (i.e. we are given the extreme points of each $P_i$). Denote the Minkowski ...
0
votes
0answers
32 views

calculating confidence intervals for a probability outcome

Suppose you have two possible outcomes, $0$ or $1$. You want to determine the probability of getting a $1$, and have confidence intervals on your answer. E.g. for $10$ runs you might have $$ \text{...
0
votes
1answer
25 views

How do I work out how many people would be selected into a specific age range by chance?

I have a sample of children that are aged 5 years up to 7 years. In total there are 2000 children from 160 centres. The purpose of this exercise was to give each child an assessment and record the ...