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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Statistics: Why do we divide by $\sqrt{n}$ for sample standard deviation

Can someone tell me if my explanations/understanding is on the right track? Suppose we have a set of variances, each of them identical, where $V_{1}(x) + V_{2}(x) + ...+ V_{j}(x) = \sigma^2$. If we wanted to take $\frac{1}{n}$-th ($n \leq j$) of…
Person
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What can we conclude from correlation?

I just got my statistics test back and I am totally confused about one of the questions! A study was done that took a simple random sample of 40 people and measured whether the subjects were right-handed or left-handed, as well as their…
Larry Wang
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Mahalanobis distance invariant

Is the Mahalanobis distance invariant with respect to arbitrary non-singular linear transformations? I mean if $C$ an arbitrary regular $(p × p)$-matrix and $b$ in $R$ arbitrary and $ \tilde{x}_n= C\,x_n +b$, is it then true that…
Rudi
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Finding $n$ using Chebyshev’s inequality

The height of a person is a random variable with variance $\leq 5$ square inches. According to Mr. Chebyshev, how many people do we need to sample to ensure that the sample mean is at most $1$ inch away from the distribution mean with probability…
Kriti Arora
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Middle School Stats Book mess up?

I am curious what everyone's thoughts are on the following problem I found in a middle school textbook I am teaching out of. The chapter is on biased and unbiased data samples. Here is the question: To find how much money the average American…
K Math
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Minimal Sufficient statistic for Uniform($\theta, \theta+1$)

We have that $\mathbf{X}$ is a random sample from Uniform$(\theta, \theta+1)$ and we want to find a sufficient statistic for $\theta$ and the determine whether it is minimal. The likelihood function is given by $$ L(\mathbf{x}| \theta) = \prod…
misogrumpy
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square root of covariance of two variables

I know that if you calculate variance, you can square root it to get the standard deviation. What does it mean / what is it called if you square root a scalar value which is the covariance of two variables?
Alan Wolfe
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Meaning of inverse temperature

I am not familiar with statistics, so when I read a book which covers statistical learning, I have a question. Here, a posteriori probability density function is defined as follows; $D_n=\{X_1,X_2,\cdots, X_n \}$ be a set of random variables and…
ddd
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Unbiased estimator of a uniform distribution

For a random sample $X_1,X_2,\ldots,X_n$ from a $\operatorname{Uniform}[0,\theta]$ distribution, with probability density function $$ f(x;\theta) = \begin{cases} 1/\theta, & 0 \le x \le \theta \\ 0, & \text{otherwise} \end{cases} $$ Let $X_{\max} =…
pkfly103
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Dropping a Lowest Score

I have a lab class, where I drop the lowest score students receive, easy enough. Except, all items are not weighted equally, (lab A might be worth 10 points, while lab B might be worth 23 points, and so on). Right now, what I do in an excel file is…
J M
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What is a confidence interval?

What are the nature and purpose of confidence intervals?
Michael Hardy
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Distribution of the sample mean of a exponential

I please ask someone to check if my calculations are right. I have $X_1, ..., X_n$ from a $\mathcal{E}(\lambda): f(x, \lambda) = \lambda e^{-\lambda x}$. I have to find the $k$ such that $P(\bar{X} \le k) = \alpha$, where $\bar{X}$ is the sample…
Aslan986
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An estimator for the c.d.f $F$ at a point $x_0$?

Problem: Let $X_1,X_2,\ldots,X_n$ be independent identically distributed random variables (i.i.d's) with common CDF $F$. Fix $x_0\in\mathbb{R}$ and find an unbiased estimator for $F(x_0)$. Show that your estimator is an UMVUE for $F(x_0)$ (i.e. a…
James
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Why does sample standard deviation underestimate population standard deviation?

Refering to this wikipedia page Unbiased estimation of standard deviation, it says that "it follows from Jensen's inequality that the square root of the sample variance is an underestimate". I do know that for the concave square root function,…
JohnC
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Logistic function passing through two points?

Quick formulation of the problem: Given two points: $(x_l, y_l)$ and $(x_u, y_u)$ with: $x_l < x_u$ and $y_l < y_u$, and given lower asymptote=0 and higher asymptote=1, what's the logistic function that passes through the two points? Explanatory…
Mino
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