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22 views

Population size and accuracy of expected value

If I have a series of populations, and a set of outcomes for these populations, how can I be certain that the observed proportions are, in fact, credible? I have investigated certain sampling methods ...
0
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1answer
37 views

Survey vs interview size

I have a survey of size 120 and 20 interviews. Can I compare the results? Both groups answered same questions. Example: let's say a question was do you like to read novels ? Can I say that 20% of ...
1
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1answer
72 views

symmetric polynomial inequality?

I put $n\ge 2$ balls of various sizes into an urn. I draw two balls (without replacement) from the urn. With each draw, I draw any given ball with probability proportional to its size. Can you ...
0
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1answer
50 views

Sample size question / margin of error

I'm a complete novice in this area - so "explaining to me like I'm 5" would be most appreciated. Essentially, I've been tasked with changing the a relevancy algorithm for products displayed on a ...
3
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0answers
180 views

Relationship between DFT and FFT/DTFT

Question 1: Assume we already know $x(t):[0,2\pi]\to\mathbb{R}$'s Fourier series $x[n]_{n=-\infty}^\infty$. Perform DFT on $x[n]_{n=0}^N$. How is the result connected to $x(t)$? WHY? Question 2: ...
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1answer
250 views

Proof that $\frac{(\bar X-\mu)}{\sigma}$ and $\sum_{i=1}^n\frac{(X_i-\bar X)^2}{\sigma^2}$ are independent

Let $X_i\sim N(\mu,\sigma^2)$ ; where$[i=1,2,\ldots,n]$ $Z_i\sim N(0,1)$ ; where$[i=1,2,\ldots,n]$ Proof that $\bar Z=\frac{(\bar X-\mu)}{\sigma}$ and $\sum_{i=1}^{n}(Z_i-\bar ...
1
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1answer
65 views

An Exercise of noncentral $\chi^2$ distribution.

Let $Y_1,\ldots,Y_n$ be independent random variables with $Y_k$ distributed as $N\sim(a_k,\sigma^2)$, and $\bar Y=\sum_{k=1}^{n}\frac{Y_k}{n}$ denote the sample mean, $S^2$ denotes the sample ...
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1answer
75 views

cumulants of non-central $\chi^2$ distribution

Cumulant generating function is defined by logarithm of moment generating function. $$K_X(t)=\log M_X(t)$$ Let $X$ be a non-central $\chi^2$ variate with parameters degrees of freedom, $n$ and ...
1
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1answer
61 views

Sampling a Population of Unknown Size

How do you sample a population whose size is not known? For example, I have a day's population from whom I need to select 1000 items from. Each hour (for one day) some number of new items (can be ...
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2answers
83 views

Probability that I am not selected in any of 2000 samples?

The population contains 100 million adults, which includes myself. Simple random sampling is used to choose a sample of 1000 adults, 2000 times, independently. I need to find the probability that I ...
1
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0answers
76 views

Problem generating random vectors with a randomized linear programming with equality constraints (weird clustering)

Summary For simulation problems, I need to be able to generate large numbers of random lists of numbers, say $x_1, x_2, \dots, x_n$ (where $n \approx 1000$), subject constraints similar to what one ...
1
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1answer
65 views

Calculate each point of my Gauss curve

I'm coding a program which calculates the confidence interval. He takes the population and a sample of the population as parameters, and the percent of people of that sample who answered "yes" to a ...
2
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1answer
71 views

Sampling labeled items on a conveyor belts

I have items on a moving conveyor belt. Every item has a label with a number that goes from $1$ to $N$; on the conveyor belt there are more than $N$ items. I have a camera above the items on the belt, ...
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0answers
160 views

Discrete approximation to a continuous probability density function

I want to approximate a continuous, finite probability density function, with a specified number $N$ of points, in the following way: If the pdf is 1-dimensional, defined over the section [0,1], then ...
3
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1answer
88 views

Maximum likelihood estimation - why is $\mathcal{L}$ not the joint pdf?

Here's an excerpt from my notes: Define the likelihood function: $$\mathcal{L}(\vec{x};\theta)=\prod_{i=1}^{n} f(x_i;\theta)$$ Where $f$ is the pdf of the distribution we're sampling the $x$'s ...
1
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1answer
696 views

probability of sample variance lying between given values

Let $X_1,\ldots,X_n$ be a random sample of size $n = 10$ from a population which is Normally distributed with mean $= 48$ and variance $= 36$. What is the probability that the sample variance of such ...
2
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0answers
69 views

Sampling probability

I have a pool of 36 samples (each is a pool itself). If I take a subset of eight samples at random from this pool, how do I calculate the probability of obtaining two of the same type of sample from ...
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0answers
66 views

Convex Hulls in Complex Vector Spaces?

I am trying to generate uniform samples over the convex hull of a set of points that are defined by a set of corresponding vectors with complex entries. In other words, I am trying to generate samples ...
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1answer
26 views

What does MSSL sampling refers to?

In a document I came across this sentence "calculation of MSSL using fixed and dynamic methods". The document itself is about sampling techniques and no other explanation is given there. I tried to ...
3
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0answers
112 views

Problems sampling from a $pdf$ over $SO\left(3\right)$

I have a probability density function over $SO\left(3\right)$, which I am trying to sample from. The $pdf$ is given as a generalized fourier series: $$ f\left(\omega,\theta,\phi\right)=\sum ...
0
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2answers
54 views

Sample $x$ from $g(x)$

I got confused with all this randomness and probability functions. I was trying to implement the rejection sampling method which (apparently) is really simple. I was reading from Rejection Sampling in ...
1
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1answer
36 views

Optimal sampling for an arbitratry area

I have a closed area (2D) of arbitrary shape and some number of sample points to take from the area. Now I would like to find optimal distribution of the sample points, so that distances from sample ...
0
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1answer
247 views

please prove the following proof related to F distribution.

Suppose $S_1^2$ and $S_2^2$ are two independent unbiased estimate of the common population variance $\sigma^2$ from two random sample of sizes $n_1$ and $n_2$ respectively. Then show that ...
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0answers
34 views

Suitable change of measure with importance sampling

I'm working on a project on Importance Sampling. When one tries to estimate the small probability $\alpha:=\mathbb{P}(X \in A)$, one can do a change of measure. There is change of measure which ...
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0answers
55 views

Continuous random sampling with replacement.

Construct a set $s\subseteq[0,1]$ by sampling points in $[0,1]$ with uniform probability density $x\leq1$ so that $|s|=x$. Interpret this as a sampling frame during which data is captured. Now, ...
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0answers
241 views

Simulate random sampling with replacement

Any ideas on how to approach this problem? (Due to Karp) Consider a bin containing d balls chosen at random (without replacement) from a collection of n distinct balls. Without being able to see or ...
2
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1answer
109 views

Monte Carlo Rejection Sampling Method

I have the following passage from a set of lecture notes I am working on that I would like to understand a little better. $\underline{\text{Algorithm for Rejection Sampling}}$: Given two densities ...
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0answers
37 views

Sphere on a grid

So, this is a little tricky kind of a question and I'm not totally sure if it's a mathematic question or a more programming one, but I nevertheless hope to find answers. I want to find out the error ...
1
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1answer
47 views

variance reduction

Say i have $n$ variables with variances $V_1,V_2,...V_n$. The sum of the variables will have a variance of $V=V_1+V_2+..V_n$ .Now if i am given N total simulations to reduce the variance V, how do i ...
3
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2answers
262 views

Simple random sampling without replacement of huge dataset

For an application I'm working on, I need to sample a small set of values from a very large data set, on the order of few hundred taken from about 60 million(and growing). Usually I use the technique ...
1
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2answers
1k views

Sampling problem with and without replacement

Find the probability of the event that number $1$ and number $7$ were chosen first and third, respectively at the experiment of choosing five numbers from this set of numbers $\{1,2,3,4,5,6,7,8,9\}$ ...
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1answer
78 views

Sample size requirements in survey

If am doing some market research and want to answer the question "What percentage of the users of a service, searched for the given service online?". Lets say I go out and get people to take a survey. ...
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1answer
1k views

Probability to choose specific item in a “weighted sampling without replacement” experiment

Given $n$ items with weight $w_n$ each -- what is the probability that item $i$ is chosen in a $k$-out-of-$n$ "weighted random sampling without replacement" experiment? Can a closed-form solution that ...
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1answer
71 views

sampling functions and effect on DFT

I'm looking for help on pointing me to the right literature.... My question is as follows... Let's assume I have a discrete function (sinusoidal in nature) sampled at N equi-spaced points. However ...
2
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1answer
514 views

unbiased estimator of sample variance using two samples

I have a couple questions, I'm hoping someone can help! Let $X_1...X_n$ is a random i.i.d. sample from a $N(\mu,\sigma^2)$ distribution, and $Y_1...Y_m$ is a random i.i.d. sample from a ...
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3answers
447 views

estimate population percentage within an interval, given a small sample

Given a small sample from a normally-distributed population, how do I calculate the confidence that a specified percentage of the population is within some bounds [A,B]? To make it concrete, if I ...
0
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1answer
122 views

How to sample from joint Bernoulli distribution?

I have done searches on google.com and here but haven't found a related one. I apologize if this is a re-post. Here is my question: I have a set $n$ of Bernoulli random numbers, and I know the ...
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4answers
402 views

Sampling from a $2$d normal with a given covariance matrix

How would one sample from the $2$-dimensional normal distribution with mean $0$ and covariance matrix $$\begin{bmatrix} a & b\\b & c \end{bmatrix}$$ given the ability to sample from the ...
1
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1answer
387 views

How to sample from a Gamma distribution with shape not integer

I'm looking for an effective method to sample from a Gamma distribution that has the shape parameter not integer. However, I found everywhere the method to sample from a Gamma with an integer shape ...
0
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1answer
217 views

Sample-based median calculation

Is there any technique to find the median of a large data set using sampling (or maybe randomized algorithms)?
0
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1answer
75 views

Determining Sample Size - Design Problem

I have a hypothetical problem were say I have a sample size of about 5000 people. I then will collect data on them say, how man calories of food they eat per day for a month. Now I can't obviously run ...
1
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1answer
39 views

Generating statistics from data samples, that are of snapshots.

My question is part math part computers but I need more of the math answer then a computer answer. I am going to be grabing snapshots of a moment of time on how a computer is performing. Because of ...
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0answers
96 views

Is it possible to calculate/impute the sample size “N” from a given mean and standard deviation?

Can anyone provide with some advice? - thank you I am required to calculate the sample size for two groups, given the following data: Total sample N (group1+group2)=583 group 1: mean=8.35, SD1.07, ...
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0answers
131 views

generating a binomial distribution

I'm trying to sample from a data set using a binomial distribution with parameters p and n. Implementation-wise, I follow these steps I generate an array containing the values of the cumulative ...
1
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1answer
53 views

Statistics and clarification of Central Limit Theorm

If I have 1,000 participants ranking on a scale of 1 to 10 regarding some object how do I interpret the confidence level and margin of error of the resulting rank? I am used to of seeing 99% ...
0
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1answer
21 views

What is the name of (1-a)*current + a*sample

Say we take a sample every time unit, we have a calibrated value which needs tracking for drift, however every sample has a given variance causing jumping if we were to use it directly as the new ...
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0answers
165 views

Giving sampling distribution of population total estimator [Homework]

Given sampling data below, Considering a Simple Random Sampling(SRS without replacement) of size 4, what is the sampling distribution of the estimators for total of y's? t1 and t2 where i) t1 is ...
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0answers
74 views

Estimating the number of observations from a set of samples

I repeatedly measure a value $S_n$ which is the sum of a set of $n$ hidden inputs. The goal is to identify the number of hidden inputs. All of the hidden inputs are driven by an experimenter ...
1
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0answers
41 views

Uniformly sample points over a circular patch of a sphere without rejection [duplicate]

Possible Duplicate: Generate a random direction within a cone A point on a unit sphere $(x,y,z)$ and an maximal angular separation $\theta$ defines a patch with an area of $\Omega = 2 \pi ...
2
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0answers
100 views

How to sample from a product-of-sums distribution?

$A$ is a $M$x$N$ matrix whose entries are positive. $x$ is a $N$ dimensional binary (i.e. consisting of $0$s and $1$s) vector and the number of $1$s in $x$ is constant. Let $y = Ax$. The distribution ...