Mathematics Stack Exchange
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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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Probability that a random variable is less than 4. (help in R)

Let $Y_1,Y_2,\ldots,Y_n$ be independent and identically distributed normal random variables with mean 5, and variance 16. Let $n=10$, use R to find $prob(\overline{Y} \leq 4)$ where $\overline{Y}$ is the mean of $Y_1,Y_2,\ldots,Y_n$. I know how to…
Chuck Franklin
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How to verify a distribution is normalized?

I have a question in which it asks to verify whether if the uniform distribution is normalized. For one, what does it mean some distribution is normalized. For two, how do we go about verifying whether a distribution is normalized or not.
Ada
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Statistics Question of unbiased estimator

Could anyone give me a hint? or way to solve?
John Smith
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Can median have decimal value for finding missing number?

I was wondering if it was possible to get the median as decimal value for finding the missing median? If there is an even number of numbers in the set, the median is the average of the two middle numbers, and the only way to find the missing number…
diya
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Factorial combination

I've just started looking over a new topic and am slightly confused on how to approach the following question.. A manager has 20 possible players to choose from for a Rugby Game. They are playing league, so need 13 players on the field and 4 on the…
Ergo
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Why are there 2 variance formulas equal?

I have found two separate definitions for variance, listed below. Could you please explain why they are equivalent? i) Variance of y $= \displaystyle \sum_{i=1}^n p_i(y_i - \mu)^2 $ ii) Variance of y $= \displaystyle \left(\sum_{i=1}^n p_i…
user95087
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Expectancy value of sale of fishballs

I am doing some elementary statistics and the following problem stumpled me a bit. A merchant receives two batches of fish cakes from two different factories, but with the same produces. Thus one can not determine witch batch came from which …
N3buchadnezzar
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Confidence in Multinomial Distributions

a response to a survey question is either yes or no. The responses are divided into ten categories, based on other information. So in category 1, there's 341 yes and 1023 no, cat 2 128 yes and 744 no, etc. I would like to calculate some sort of…
user94549
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Given a set of intervals, when an element is not in said set when is that considered statistically suspicous?

So I am working on a project and the question came up: How far out of the range of a bunch of intervals $ \{ [a_i, b_i] \}^N_{i=1}$, when is it suspicious when $c_i \not \in \{ [a_i, b_i] \}^N_{i=1}$. Because we are trying to perform hypothesis…
OncoMath
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Is the exponential mean weight average (EMWA) a Pearson mean?

The Pearson mean is a weighted mean defined as $$m_t = \frac {\sum_{i=0}^t w_ix_i} {\sum_{i=0}^t w_i}$$ The exponential mean weight average (EMWA) is the following recurrence where $0 < \alpha <1$. $$m_t = (1-\alpha)m_{t-1} + \alpha x_t = m_{t-1} +…
chmike
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Consider the joint pdf for $X$ and $Y$ given by $f(x,y)=3x, 0 \le y \le x \le 1.$ What is the probability $P(0 \le X\le 0.5, 0.25 \le Y)$?

this should be a pretty easy one, but I cannot for the life of me get the supposed answer of $\frac{5}{28}$. What are my limits of integration supposed to be? I have tried a million different limits of integration, but the one that seems to make the…
JackReacher
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How to generate data points which follow "Tweedie exponential dispersion process"??

We are trying to generate data points which follow "Tweedie exponential dispersion process(TED)". Here we are giving approximated PDF of TED process, which is expressed as $f(y)=\sqrt{\frac{\lambda}{2\pi t^{1-\rho y^\rho}}}exp\{-\frac{\lambda t…
Aritra Mandal
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Definition of a Statistical model

My understanding of the definition of a statistical model is a probability space $(\Omega,\Sigma,p)$, a random variable $X:\Omega\to\mathbb{R}$, and a collection of probability measures $\mu_{\theta}$ on $\mathbb{R}$, where $\theta$ is a…
user124910
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Proving empirical distribution function is the effective estimator for cumulative distribution function

Let $\hat{F}_{n}(x)$ be the Empirical Distribution Function (EDF), where $X_{1}...X_{n}$ is an iid sample: $$ \hat{F}_n(x) = \frac{1}{n}\sum_{i=1}^n1_{\{X_i\leq x\}} \quad \forall x\in\mathbb{R}$$ It can be shown that $\forall x$…
israil_doberman
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Finding the solution of MME Problem

Suppose $X_1,X_2,\ldots,X_n$ be a random sample of distribution with probability density function $$f(x\mid\theta) = \theta x^{\theta-1},\quad 0\lt x \lt 1,\quad 0\lt \theta \lt \infty$$ how can i find MME of parameter $θ$? My working: $E[\theta…
lakshmen
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