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.

37109 questions
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Central limit theorem, taking repeated measurements

I'm using a book from R.J.Barlow, a stat book for science students. I was confused by some of the wordings in the book.The first two paragraph are some true statements.The bottom paragraph confused me most. Suppose you took n measurements…
el psy Congroo
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Statistics question to apply bell curve to formula

I am trying to write a formula that would give a person a score, based on a formula. It's for a video game, and I have worked up a formula using aggregate stats like total kills divided by total deaths, win percentage, etc. They are all ratios. I…
bladefist
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Expectation and random sample

Let $X_1,X_2,...,X_n$ be a random sample of size $n$ from a population $N(\mu, \sigma^2)$ with $\sigma^2=4$. Further assume that $\mu \sim N(0,1)$. Find $E[\mu|X]$ and $E[(\mu - E[\mu|X])^2 |X]$. Find the precision of the normal distribution. Find…
Betty
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General Definition of Likelihood Function

I am wondering if there is a way of generalizing the likelihood function of some parameters $L(\theta | \mathbf x), \theta \in \Theta$ given some data $\mathbf x$ that has been observed coming from a distribution on $\mathbb R^n$, say $\mu$, so that…
guy
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how to properly calculate difference in percent

Suppose, you have x=8 y=10 Then y is 25% more than x, if x is used as the "base" value. If y ist the base, then x is 20% less than y. So if I want to say, that the difference between x and y is ... percent, what value could I use? I can think of…
Amelse Etomer
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Minimally Sufficient Statistic for Bivariate Distribution

Say you have: $f(x_i,y_i)=\lambda \mu \exp\{-\lambda x_i-\mu y_i\}$ However you only observe: $Z_i=\min (X_i,Y_i)~$ & $~U_i=\begin{cases}1~\text{if}~Z_i=X_i \\ 0~\text{if}~Z_i=Y_i\end{cases} $ We are asked to find a minimally sufficient statistic…
ActuariallyImpaired
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What does "$.05$ irrespective of the value of $\hat p$" mean?

I have a statistics question that says "What sample size would be required for the width of a $99$% confidence interval to be at most $.05$ irrespective of the value of $\hat p$?". But I'm not sure what irrespective is refering to. I tried to figure…
TheHopefulActuary
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Means and Variances

For a laboratory assignment, if the equipment is working, the density function of the observed outcome $X$ is $$ f(x) = \begin{cases} 2(1-x), & 0
Danathon
  • 355
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Likelihood Ratio Test

I am having a hard time understanding what this following question is asking. I do not have any clue pn how to start it. Any help would be great. Thanks in advance. Let $X_1,X_2,...,X_n$ be a random sample, $X=(X_1,X_2,...,X_n)^T$, $X=x \in B…
Betty
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Why the area under the probability density function curve is probability

Why is the area under the probability density function(PDF) curve gives probability?
Ankit Das
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Find an estimator

I'm self studying statistics, and this is one hw problem that I'm getting stuck at. Suppose in two independent trials with prob p of success, we observe X successes. Find an unbiased estimator T(X) of the function $g(p)=p^2$ Is it simply $(X/2)^2$?
Dzung Nguyen
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Pdf of the n-fold transformation of uniform random variables?

For independent variables $X_1$,$X_2$, $X_3$, $...$, $X_n$ with $n>2$, all uniformly distributed in the interval $[0,1]$ and if $X_1 < X_2 < ... < X_n$ I am trying to find the pdf of $Y_n$ = $\frac{X_n}{(X_1 X_2 \dots X_n)^\frac{1}{n-1}}$ How should…
user97019
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Unbiased estimator and Variance

I am having a hard time trying to solve this problem. I don't know how to start it. Any help would be greatly appreciated. Let T be any unbiased estimator of $\tau(\theta),$ and let $W$ be a sufficient statistic for theta. Define $\phi(W)=E[T|W]$.…
Betty
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How to prove MLE of variance is biased

How to show the $$ E(\Sigma_{MLE})=E\left(\dfrac{1}{n}\sum_{i=1}^{n}({x}_{i}-{\mu}_{MLE})({x}_{i}-\mathbf{{\mathbf{\mu}}}_{MLE})'\right)=\dfrac{n-1}{n}\Sigma $$ Where ${\mu}_{MLE}=\dfrac{1}{n}\sum_{i=1}^{n}{x}_{i}$ and ${x}_{i}\sim…
Ada
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