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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Question about correlations in statistics

x: 1,2,3,4,9,10 y: 12,2,3,5,9,11 What feature of the data is responsible for reducing the correlation to this value despite a strong straight-line association between x and y in most of the observations?
Momoko
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In statistics what does mutually exclusive mean?

For homework a question related to Venn diagrams is 'Are the probabilities of having not used a spinner and not tossed a coin in the game mutually exclusive' Don't know what is meant by it so can't answer it with out your help
Ray Kay
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Inconsistency in two-sided hypothesis testing

Suppose you have two sets of data with known population variances and want to test the null hypothesis that two means are equal, ie. $H_{0}: \mu_{1} = \mu_{2}$ against $H_{1}: \mu_{1} > \mu_{2}$. There's a certain way I want to think about it, which…
Mr. G
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In general, $\textit{Var}(X) = E(X^2) - [E(X)]^2$

This is from page 25 of this book: In general, it may be shown that $$\textit{Var}(X) = E(X^2) - [E(X)]^2$$ I can't remember ever seeing that "In general" elsewhere. So if this identity only holds "in general" are there cases where…
JasonMond
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Proof the concave transformation of the tail distribution is always above the tail distribution

I need to prove that for a given continuous non-decreasing distribution $F_X(x)$, and a concave non-decreasing distortion function $g(.)$ defined on $[0,1]$, the following holds: $$g(1-F_X(x)) \ge 1-F_X(x)$$ We know that $g(0) = 0$ and $g(1) =…
blah_crusader
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Problem of Statistics

Let $x$ be a variable assuming values $1,2,\ldots,k$ and let $F(1)=n,\ldots,F(n)$ be the corresponding cumulative frequencies of the 'greater than' type. Show that $$\text{Mean of }x=\frac{ F(1)+\cdots+F(k) }n.$$
soumajit das
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Finding midpoint in class interval to calculate mean for cumulative frequency graph.

In a cumulative frequency graph (or histogram), the data is often given in class intervals. To calculate the estimated mean of the data, the formula is: $$\frac{\sum m\cdot f}{\sum f}$$ where $m =$ midpoint of the class intervals and $f =$…
user9856
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Correct Way to Break Up Range Into N Approximately Equal Discrete Bins

This seems simple, but none of the solutions I've tried work well. For example, for a range [0, 67), how can you split it up into 20 approximately equal sized discrete bins without introducing significant artifacts due to rounding? I've tried the…
JDiMatteo
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Normal probability distrubution.

any student who scores in the top 4% of students on the SMRT standardized exam. SMRT scores have a mean of 260 and a standard deviation of 22. What score does a student need to attain in order to receive the scholarship worked problem this…
barb
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Mutual Exclusivity

Suppose that a study is being done on all families with one, two, or three children. Let the outcomes of the study be the genders of the children in descending order of their age. A. List sample space M = Male F = Female {M, F, MF, MM, FM, FF, MMM,…
Need Help
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How to calculate probabilities of win, draw and loss based on the ELO system

Consider one game between two opponents (I am actually thinking about chess but it doesn't have to be that). The ELO rating system gives the expected score $E_A$ and $E_B$ for both players. That is $$E_A=Pr(A\ wins)+\frac12Pr(draw)+0Pr(A\…
Georgy
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if the probability density of $x$ is given by

If the pdf of $X$ is given by $$f(x)=\begin{cases} 1+x & \text{for } -1< x \leq 0 \\ 1-x & \text{for } 0
Fernando Martinez
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Name That Statistical Function

I have a matrix $ M= \begin{pmatrix} -a_1 & b_{21} & b_{31} \\ b_{12} & -a_2 & b_{32} \\ b_{13} & b_{23} & -a_3 \end{pmatrix} $ And a function $f$ which gives $ f(M)= -\frac{a_{1}^2}{9}+\frac{a_{1} a_{2}}{9}+\frac{a_{1} …
Richard
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Joint PDF transformation

I think I know how to do this but I just want to make sure that it's 100% correct. $X_1, X_2$ are i.i.d. random variables with distribution EXP(1) f($x_1, x_2$) = $e^{(-x_1-x_2)}$I(x >= 0) Question: Find the joint PDF of $T_1$ = min($X_1, X_2)$ and…
user3251256
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Confidence Lower Bound for a random sample.

IQ scores are desinged to be normally distributed with standard deviation 15. Below are the IQ scores of a random sample of 30 seventh grade girls in a Midwest school district. 114, 100, 104, 89, 102, 91, 114, 114, 103, 105, 108, 130, 120, 132,…
nonremovable
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