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

0
votes
0answers
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 ...
0
votes
0answers
15 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 $P(0<...
2
votes
1answer
53 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
16 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
204 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
46 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 x_{i}...
0
votes
1answer
40 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
24 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 $...
2
votes
1answer
31 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
13 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
38 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
73 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
44 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 $Y=(...
0
votes
0answers
11 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. ...
0
votes
0answers
30 views

Sampling the Sin(x)/(x) Function

Say we have $$x_c(t) = \frac{sin(\pi t)}{(\pi t)}$$ $x_c(t)$ has a maximum frequency of $\omega_M = \pi$. According to Nyquist's Theorem, this signal can be perfectly reconstructed from its samples, ...
0
votes
1answer
122 views

2 simple statistics questions regarding probability and means.

Fire alarms go off in the engineering building an average of 13 times per year. Find the probability of more than one fire alarm going off in the month of December. For this one, I am uncertain on ...
0
votes
2answers
25 views

What's the formula to get the x2 in this chi-square table?

I'm just wondering what's the formula to get the x2 answers in this table.
0
votes
0answers
14 views

Stratified sampling

In general, is there an optimal number of stratas to use when employing the Monte Carlo variance reduction technique: "Stratified sampling"?
1
vote
0answers
38 views

Generate Uniformly Random Points on a Transformed Sphere

I have a sphere transformed by an affine transformation (represented as a 4x4 matrix). How should I get uniformly distributed points on the transformed sphere's surface? Note that the obvious thing--...
0
votes
0answers
22 views

Statistics- Why is T being used over Z here?

"In their 1992 study of human internal body temperature, Mackowiak, Wasserman and Levine, their sample mean, x = 98.25 with standard deviation = 0.73, led them to a hypothesis that human internal body ...
0
votes
1answer
104 views

What does the conclusion with confidence interval mean, non-statistically speaking?

There is a manufacturer who told me that they tested devices in the batch based on 95% confidence level, 5% confidence interval/margin of error and 50% distribution. So from 1500 devices, they tested ...
0
votes
1answer
23 views

Asymptotically unbiasedness of an weighted estimator

Consider a Markov chain on a state space V with size N, and let $\pi(v_j) = \sum_{v_i \in V} \pi (v_i)P(v_i,v_j)$ be the stationary distribution, where $P(v_i,v_j)$ is the transition probability. ...
0
votes
0answers
59 views

Sampling from a probability distribution

We are given the probability density functions for the random variables $Y_i$ ($i=1 \ldots N$): $$ f_i(t) = \begin{cases} 0 & t \le 0\\ \frac 1t \cdot (2\pi\Sigma_{ii})^{-1/2} \exp\...
0
votes
1answer
53 views

General equation for sampling without replacement probability

Looking at a preparatory exam, I'm a little dumbfounded by a question on probability. There are $19$ balls in a box: $5$ red, $3$ white, and $11$ blue. The question is: what is the probability of ...
0
votes
0answers
16 views

bradley-terry generating synthetic data

Im trying to generate synthetic data by Bradley-Terry model perspective. I think I need to steps first generate skill parameters and then generate the matrix showing number of winning of ith player ...
1
vote
1answer
58 views

Rejection Sampling From Conditional Distribution

I am familiar with rejection sampling in the univariate case, where we have a proposal $h(x)$ (which we can sample from) for the target density $p(x)$ such that $p(x)<Mh(x)$ at all $x$. We sample $...
0
votes
0answers
12 views

Data filtering VS Sampling Process

I am writing on a write up of how i obtained my sample from a large population. But I am contemplating whether I should categorize them under 'data filtering' or a 'sampling process'. Any idea what ...
3
votes
1answer
68 views

Integrating an infinite series of the Dirac function

I am given the following sampling signal function, where $\delta$ is the Dirac delta function, t is time, and Ts is the sampling period. First, I am asked to plot the signal. I do not understand ...
2
votes
2answers
47 views

Question about the expected number of sampling until one item out of k is found

) I have k items (let's say balls) that all have a different color, but I do not know the color until I pick them. I would like to know how many balls I have to pick until I get one with a specific ...
0
votes
0answers
23 views

Maximum Sample value for a given Sample Size and Distribution

Suppose a sample size of 100 samples are drawn randomly from an Exponential distribution. For a given mean of the exponential distribution (say $\mu$), what could be the maximum possible sample value ...
0
votes
0answers
60 views

right way of weighting sampling for a distribution?

Recently I have read a paper, in a part of that the authors try to sample from the distribution $p(\alpha|\tau )=P(\tau | \alpha)\times p(\alpha | \alpha_0)$ where $\tau$ is some evidences in the ...
1
vote
0answers
22 views

Express covariance function of a sampled process as a fourier transform (help with proof)

I'm wrestling with this theorem in my 'stationary stochastic processes' course.It's about sampling of a continous process and a way of rewriting the covariance function of the sample(I'm not entirely ...
1
vote
1answer
28 views

Sample size and confidence interval

We want to produce a $0.90$ confidence interval for the proportion of vegetarian recipes at one cookbook. We will use simple random sampling without replacement to select a sample of $2311$ ...
2
votes
1answer
92 views

How to calculate error margin on measured number of occurd events when sampling

We are measuring the number of times a certain event happens. We do this with the help of sampling, so that we only report events with a probability p. For example p=0.01 would result in about 1/100 ...
1
vote
1answer
18 views

Matching: Calculated data vs. sample from the real world

I have a small set of measured values from the real world. It is a rather small sample (10 from 1000). Actually there is no way for me to increase the sample, it is just possible to use 10 values ...
0
votes
1answer
93 views

Generation of random variable from a complicated CDF

Suppose I am given a CDF of a distribution, given by $F(x) ∝ \int_0^1 x^y e^{-y} dy.$ Here,'x' ranges from 0 to 1. How do I generate a random variable from this distribution?
0
votes
1answer
28 views

Goodness-of-Fit tests for Multinomial and Binomial Data

A box has 4000 red, 5000 blue and 1000 orange balls. A selection of 70 balls is made, with 25 reds, 35 blues, and 10 oranges being observed. Can one essentially prove that the selection was NOT a ...
0
votes
2answers
89 views

What's the difference between MCMC and particle MCMC?

Markov chain Monte Carlo (MCMC) methods are a class of algorithms for sampling from a probability distribution based on constructing a Markov chain that has the desired distribution as its equilibrium ...
0
votes
1answer
39 views

Generating Random Variates from CDF

Suppose I am given a CDF of a distribution, given by $F(x) \propto x + x^2 + x^4 + x^7$. How do I generate a random variable from this distribution?
0
votes
1answer
39 views

Poisson sampling

Suppose I have a pdf $f(S)$. $f(S)$ describes the size of firms in the economy. Also define the Bernoulli variable $X_{f} \in \{0,1\}$ where $P(X_{f}=1)=g(S_{f})$ and $P(X_{f}=0)=1-g(S_{f})$. $S_{f}$ ...
3
votes
2answers
125 views

Selecting k distinct numbers from an array with increasing probability distribution

I have to select k distinct numbers from an array such that probability of a number getting selected is more if it is at the end of the array (probability increases linearly). I'm thinking of ...
0
votes
1answer
154 views

Finding Probability of picking one ball out of N balls.

presented with n identical balls, one with a prize in it. Picks each ball out idependently one at a time till gets prize. I need to find the mean and variance of the number of balls needed to pick ...
1
vote
1answer
28 views

Biased sample from biased sample

A webpage has users, where each user has a number of projects uniquely assigned to him or her. I want a random sample of users by randomly sampling projects and then taking the users connected to this ...
1
vote
2answers
63 views

95% Confidence Interval Problem for a random sample

The sample mean of a random sample of $25$ observations is $9.6$ and the sample variance is $22.4$. Derive a $95$ confidence interval for the population mean. I calculated the following: Confidence ...
2
votes
2answers
50 views

Resampling operation

I am reading from an arXiv.org paper the following math text: "Let $x\in \{−1, 1\}^I$ be random and uniform, and let $y$ be obtained from $x$ by resampling each coordinate with probability $\...
0
votes
1answer
36 views

Can we use a single sample from a population to create confidence intervals, do hypothesis testing, etc.?

When conducting confidence intervals, hypothesis testing, and ANOVAs are we using the sampling distribution with multiple samples as opposed to a single sample? Are there cases where we use just a ...
0
votes
0answers
35 views

Distribution or samples of a function of a random variable

OK I edited the question: I have the following setup: Stereo camera setup with two images I, I'. 4 1-dimensional random variables (each corresponding to the inverse depth value of a pixel on an ...
3
votes
0answers
67 views

Intuition of the Hessian of the Log Barrier Function

I have a convex polytope defined by $\mathbf{Ax \leq b}$ (row-wise) The log-barrier function is defined as: $$\phi(x) =-\sum{\log(b_i - a_ix)}$$ The Hessian of the log-barrier is : $$\nabla^2\phi(...
0
votes
1answer
33 views

Sampling with independent probabilities

I'm looking for one specific sampling method that decides about inclusion probability of each item regardless of existence of other elements. As an example given 0.5 as the inclusion probability, it ...
0
votes
1answer
39 views

How does sampling affect the distribution of frequencies of individual types?

Consider a population of size N in which individuals can be of x different types. Take a sample (with replacement) of size ...