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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Expected value of a minimum?

One of the problems of my Statistics assignment requires me to calculate the expected value of a minimum. Here's the situation: The following density function is given: $f(x) = \frac{\theta}{x^2}$ where $x\ge\theta$ and $\theta>0$ I have to…
Maria Ramos
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Chances of someone being of a certain gender at websites

I have 2 of websites and I know the chances of a visitor being a female or male. Let's say I have 2 website where the chance of a new visitor being a female is 80%. If the visitor comes on website 1 I know the chance of that visitor being female is…
Kevin
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Standard Deviation Annualized

Say I take the standard deviation of 730 data points, representing two years worth of data. How would I convert this standard deviation to an "annualized" one? Thanks for the help.
icobes
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Does an exponential model fit my data?

I am measuring accumulation of a fluorescent-tagged protein at a particular location within a cell over time. In previous experiments that I have performed, I see a standard exponential distribution where the fluorescence intensity reaches a…
Josh
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Why sample statistics converge to the right parameter

We know that for sample/empirical distribution function $F_n(x)$ we have that a) $F_n(x)\xrightarrow[p]{}F(x)$ (pointwise convergence) b) $\dfrac{\sqrt{n}(F_n(x)-F(x))}{\sqrt{F(x)(1-F(x))}}\xrightarrow[d]{}N(0,1)$ c) $F_n$ converges uniformly in…
An old man in the sea.
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The definition of the sample standard deviation

I am reviewing the statistic. I read the book "Probability and Statistical Inference" which is written by Robert V. Hogg and Ellit A. Tanis. There is a statement in the book says that: (Section: The Mean, Variance, and Standard Deviation) The…
bfhaha
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Show that the posterior density of ($\mu$, $\tau$) is equal to $f(\mu, \tau | x_1, ..., x_n) = f(\mu| \tau, x_1,...,x_n)f(\tau|x_1,...x_n)$

Here is the full problem: Let $X_1,...,X_n$ be a random sample from a $N(\mu,\sigma^2)$ distribution. Let $\tau = \sigma^{-2}$, so we can write the distribution as $N(\mu,\tau^{-1})$. Suppose the prior for $(\mu,\tau)$ has density $f(\mu,\tau)…
user18589
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Help with question on joint Gaussian distribution

Does anyone know how to start this question? Let random vectors $x,u,v$ have joint Gaussian distribution, and $u,v$ be independent. Show that $E(x|u,v)=E(x|u)+E(x|v)-E(x)$.
kkk
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Is there any statistical method to compare two curves?

Is there any statistical method to visually compare two curves? What is the best and correct way to compare two similar curves and calculate the error/difference in percentage? I have created a program that generates a curve of a column base using…
Riko
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Why are samples always taken from iid random variables?

In most mathematical statistic textbook problems, a question always ask: Given you have $X_1, X_2, \ldots, X_n$ iid from a random sample with pdf:(some pdf). My question is why can't the sample come from one random variable such as $X_1$ since $X_1$…
lord12
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Inverse Gaussian distribution

Let $X_1,....X_n$ be a random sample from the inverse Gaussian distribution with pdf $$f(x|\mu,\lambda)=\left(\frac{\lambda}{2\pi x^3}\right)^{1/2} \exp\left(\frac{-\lambda (x-\mu)^2}{2 \mu^2 x}\right),\quad0 \lt x \lt \infty$$ For $n=2$, show that…
Yang
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Getting a single-value estimation of trust in a computed mean

Suppose I have a number N of independent ratings of a given item, where each rating is an integer between 1 and 7 (inclusive). For simplicity sake, let us assume the ratings are normally distributed, though the mean and stddev will be different for…
Jon Smark
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reason of the definition of the covariance

The covariance of two random variables $X$ and $Y$ is defined to be $${\rm Cov}(X,Y) = E[(X-E[X])(Y-E[Y])]. $$ I don't understand it, if someone could explain me this please. Why does this value tell us of some relation about $X$ and $Y$?
Daniel
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Proof of $ \text{Var}\,\left(\sum_{i=1}^{n}g(X_i)\right)=n\left(\text{Var}\,g(X_1)\right).$

I have a question about part of a proof of a Lemma in a book (Casella's Statistical Inference) I'm reading. This it how it goes. Let $X_1, \cdots ,X_n$ are a random sample from a population and let $g(x)$ be a function such that…
Nana
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