Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [statistics]

Mathematical statistics is the study of statistics from a mathematical standpoint, using probability theory and other branches of mathematics such as linear algebra and analysis.

Statistics is the science of the collection, organization, and interpretation of data. It deals with many aspects of data, which includes the planning of data collection in terms of the design of surveys and experiments. (From Wikipedia)

More specifically, mathematical statistics is the study of statistics from a mathematical standpoint, using probability theory as well as other branches of mathematics such as linear algebra and mathematical analysis. (From Wikipedia)

For questions which are more generally about collecting and treating data, it is advised that you post your question on Cross Validated and DSSE.

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How many items to acquire to get a full collection? (random chance involved)

The problem: My daughter wants to have a collection of certain Kinder Surprise toys. There're 10 different toys in this series. Assuming the chances of getting each toy are equal, how many Kinder Surprises should I buy to get her a full…
Th334
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normal distribution question?

I was wondering if anyone could explain how to use the mean and standard deviation of a normal distribution to determine the top 5% of population? -It is for homework, but I wont post the actual questions since I want to do them myself. Just needing…
shari
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Why use Euclidean distance in linear model?

The method of least squares is the most basic method in statistical linear models. For the simplest linear model$$Y_i=\beta_0+X_i\beta_1+\epsilon_i$$we are looking for $\beta_0$ and $\beta_1$ that minimizes the Euclidean distance…
abc1m2x3c
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Can you really tell the relationship between mean and median in a skewed graph?

In two old statistics textbooks, I found the following pictures:- Without any explanation, they both inferred the following:- When it is right skewed (as in fig. 3.2), mean > median. (And is the otherwise for the left skewed.) I wonder if the…
Mick
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What is the $k$th factorial moment of the binomial distribution?

I'm not sure what to do from here. $$E[x(x-1)(x-2)\ldots(x-k+1)]=E\left[x!\over k!\right]={1\over k!}\left[\sum x!p(x)\right]={1 \over k!}\left[\sum\frac{n!}{(n-x)!}p^{x}q^{n-x}\right]$$
Cloud54
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statistics - expected and probable numbers

The task: The number of oil tankers, arriving at a certain refinery on one day, follow a Poisson distribution with the parameter $u = 2$. The present harbour facilities can serve 3 oil tankers a day. If more than 3 oil tankers arrive on a given day,…
Mikkel
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The inverse variance is proportional to the sample size?

Interested in meta-analysis I found the lecture notes http://www.uazuay.edu.ec/cibse/lecture_notes.pdf I understand that it makes sense in a meta-analysis to assign different weights to different studies. Personally I find it natural to weigh by…
wood
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Which is the better estimator for the mean?

measurements x1, x2, x3 from three independent runs of an experiment with variance sigma-squared. Which is the better estimator for the mean? (x1+x2+x3)/3 or (x1+2x2+x3)/4 I am having trouble with this homework problem. I think the first one would…
SamHaim
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How to generate a good guess from other guesses, if the average has already been taken?

There are votes two days from now* and someone made an excel sheet where people at work would make their guesses on the outcome. Since I'm not from this country, I had no idea what to do and decided to be super clever and make my collumn just the…
Nikolaj-K
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Calculating linguistic diversity of a text with respect to size

I'm doing linguistics work and I'm trying to make a measure of linguistic diversity in a text. A simple calculation seems to be linguistic uniformity (diversity) = number of words / unique words But this must "privilege" shorter texts like poetry…
Laurence
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method of moments of an uniform distribution

Let $ X_1, ... X_n $ a sample of independent random variables with uniform distribution $(0,$$ \theta $$ ) $ Find a $ $$ \widehat\theta $$ $ estimator for theta using the method of moments Thanks I think using the indicatrix used in this type…
Daniel
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Given mean and standard deviation, find the probability

Lets say that you know the mean and the standard deviation of a regularly distributed dataset. How do you find the probability that a random sample of n datapoints results in a sample mean less than some x? Example- Lets say the population mean is…
IgneusJotunn
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Median of a set of Integer

The median of a set containing odd number of integer is the middle element after sorting. What about the case of even number of terms. Some places mention of average of the two middle value, but I heard that precise definition allows any number from…
Shamim Hafiz - MSFT
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Show that $T$ is an unbiased estimator

I'm given the following exercise; Let $X_1$,$X_2$,...,$X_n$ a sample from Uniform distribution $U(\theta,2\theta)$, $\theta>0$, with PDF $$f(x)=\frac{1}{\theta}, \theta
John0207
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Understanding degrees of freedom

Please provide guidance for the following question. Which of the following is/are correct? $1.$ A free particle in $\mathbb R^3$ can have infinite degrees of freedom. $2.$ The number of degree of freedom of $N$ particles is greater than $3N$. $3.$…
aarbee
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