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.

learn more… | top users | synonyms

-1
votes
0answers
10 views

What star rating is representative of this distribution?

100 people vote. They can vote 1, 2, 3, or 4 stars. Distribution: 1 = 33, 2 = 26, 3 = 12, and 4 = 28. What star rating would you say is "representative" of these 100 people: 2.36 (2), the average, ...
-1
votes
0answers
10 views

Sampling Distributions. Statistics [on hold]

I'm stuck in this problem: Problem Picture I did the literal a and b, but the rest of them I don´t understand, the reason why.
0
votes
1answer
13 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 ...
0
votes
0answers
9 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 $n$ ...
1
vote
0answers
15 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 ...
0
votes
1answer
28 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 $100$ ...
0
votes
0answers
11 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? ...
1
vote
1answer
55 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
votes
0answers
56 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 ...
0
votes
1answer
16 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
vote
1answer
21 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 ...
0
votes
0answers
28 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$, ...
1
vote
0answers
13 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 ...
0
votes
2answers
24 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 ...
0
votes
0answers
18 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 $E(|X_r - X_r'|)$, ...
-1
votes
0answers
30 views

Bound on number of random variables from their sum

Given $X_1,\dots, X_n$, independent random variables bounded by the interval [0,1], their sum $S_n$ can be bounded using Hoeffding's inequality, for every $t$: $$\mathbb{P}(|S_n - \mathrm{E}[S_n]| ...
1
vote
1answer
29 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
vote
1answer
22 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. ...
4
votes
0answers
39 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 ...
0
votes
1answer
17 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 ...
0
votes
0answers
9 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 ...
0
votes
0answers
6 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
vote
1answer
35 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 ...
0
votes
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 ...
0
votes
0answers
21 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 ...
2
votes
2answers
44 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
vote
1answer
27 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. ...
0
votes
0answers
26 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 $\pi$. ...
0
votes
0answers
30 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 ...
0
votes
1answer
56 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 $E(\bar X_n)$, $Var(\bar X_n)$, ...
0
votes
0answers
20 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 ...
0
votes
0answers
10 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 ...
0
votes
0answers
48 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 ...
0
votes
0answers
14 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 ...
0
votes
0answers
24 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: $N_i$; $\bar{X}_i$ ; ...
0
votes
0answers
26 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 ...
0
votes
0answers
13 views

Finding probability given a sample from 36 with a given distribution

Let the sample mean and variance be based on a random sample of size 36 from $N(4, 121)$ distribution. Find $P(0 < X < 8, 40 < S^2 < 160)$. Since they are independent it would be ...
2
votes
1answer
43 views

How to find the variance of a random sample with exponential distribution?

This will seem like a very simple question to many of you; but I cannot understand part of the solution, so to give context I have had to unfortunately resort to typing the whole thing out, apologies. ...
0
votes
0answers
10 views

Probability of a difference dependent samples, normal distribution but unknow parameters

I have two samples, $X_0, Y_0$, containing the marks in a test before and after training course over the same workers, thus dependent paired samples. X, Y can be considered Normal, with the same ...
0
votes
0answers
103 views

p-value of uniformity of given distributions,Matlab

Given a vector of real numbers $[a_0,...,a_n]$, how do I find the $p$-value (in Matlab, say) that it is drawn from the uniform distribution over [0,1]? I.e. $H_0$ is the hypotheses that it is drawn ...
3
votes
0answers
35 views

Uniformly sampling points from inside a region of cube

Let the dimension n=200 be fixed. The problem I am interested in is sampling points in n-dimensional Euclidean space uniformly from the region $$ \sum_{i=1}^{n} x_{i}\leq 1, $$ where $0\leq ...
0
votes
1answer
30 views

Variance of sample mean difference

I have encountered this a variation of this problem as a test task for a job interview. It's been long since I last encountered probability theory, so I couldn't solve it. Still, it deprived me of ...
0
votes
1answer
18 views

How to express in an equation, a constant plus a random sample?

Suppose I have a Beta distribution, and want to express in an equation a random sample from this distribution. I could say $x \sim Beta(\alpha, \beta)$. Now, consider the case when $x$ is a constant ...
1
vote
1answer
26 views

Bacterial Sampling : Dependent event

I have a question regarding distribution of bacteria in wells: I have a tube that contains 200ul of 5000CFU/ml of bacterial solution. If I have 20 tubes to which I will add 10ul of bacterial sample ...
0
votes
0answers
12 views

Compute frequencies present in a sampled signal

I have a signal $$ X(t) = \sum^3_{k=1} A_k \cos (2\pi f_k t + \phi_k), -\infty < t < \infty $$ where $E[A_1^2] = 1, E[A_2^2] = 4, E[A_3^2] = 1$ and the phase functions are uniformly ...
0
votes
0answers
31 views

Importance of uniform stationary distribution

When I study Markov chain (or sampling) related papers, most of them emphasize "uniform stationary distribution". But, I can't sure why it is important for Markov chain problems or randomized ...
0
votes
0answers
45 views

Prove that $ES \leq \sigma$, with S being a random sample

Assume we have a random sample S of (X1,...,Xn) from a population with finite variance $\sigma^2$. Prove that $ES \leq \sigma$ How would you prove this? Is there some way to do this using Jensen's ...
2
votes
0answers
43 views

Ratio estimator in sampling

Let the population $U=(1,2,3)$. We want to estimate $R=\frac{\mu_y}{\mu_x}$.Consider the estimators $$\hat{R_1}=\frac{\overline{y}}{\overline{x}},\hat{R_2}=\frac{\overline{y}}{\mu_x}$$ where ...
0
votes
0answers
28 views

How many random points so i need to pick such that I can truly represent the dataset I am sampling from?

How many random points do I need to select to truly represent a set of points? I have around 750 points in my dataset and I'm currently randomly selecting 300 points. I know the dataset is not large ...
0
votes
0answers
10 views

How come uncertainty adds up without squaring it?

I'm currently trying to sum measurement with unknown uncertainty. My plan is to make an experiment and try to measure multiple time the same sample and figure the variance of each of my measurements. ...