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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How do you find the mean and variance with new observations?

When given a mean and variance of a sample, without knowing the observations, how would you then find the new mean and variance given more observations? Any help with this would be much appreciated. Thank you in advance
Justin
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How to a sample of a time series of zeros and ones with given autocorrelation function?

Let's say, I have an autocorrelation function: $$C(\text{lag}) = \text{lag}^{-\gamma}$$ How can I generate a sample of a time series of, say, $0$'s and $1$'s, such that their sample autocorrelation function matches the given one? The given function…
user61192
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What is Kendall Tau's co-efficient and Pearson co-efficient

I came across these two terms in a paper about Natural Language Processing. So I looked both of them up on the net and couldn't understand a thing. So far I think their a method of comparing two quantities that have some kind of relationship with…
cjds
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Statistics $E[V]$ Problems

I have 2 statistics problems I am stuck on. Can anyone help me? Use the definition in Expression 3.13 to prove that $V(aX+b)=a^2\sigma_x^2$. [Hint: With $h(x)=aX+b$, $E[h(X)=a\mu+b$ where $\mu=E(X)$.] Expression 3.1…
D. Wei
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How much does the Top 1% have?

Please consider the following problem and my answer to it. The answer seems to low to me. Is my answer right? Thanks, Bob Problem: The median net worth of a certain population is $97K$. To be in the top $5\%$ you need to have a net worth of $2387K$.…
Bob
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What is the statistically natural way to center the logit-scale around a given value?

I would like to find out the formula for CandidateAbility used in the European PISA-test, which tests 9th grade pupil's abilities. Unfortunately the agency which publishes the results does not provide many mathematical facts. They say they use a…
Peter
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If T follows a t-distribution them prove that U=T^2 follows an F-distribution

Is this correct is there a more elegant way to do this
Maths2020
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Get quartiles and a half of the data

The following table shows a frequency distribution of the scores obtained in a test. Punctuation (3, 4] (4, 5] (5, 6] (6, 7] (7, 8] (8, 9] (9, 10] Number of participants 2 4 10 20 40 35 9 (a) The highest score…
Fernando
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Skewness - Zero

Why is the skewness of the samples $[ 1,\,2,\,3,\,4,\, 5,\, 6,\, 7,\, 8 ,\, 9 ]$ zero? Of course, it follows from definition, $\displaystyle E \left[\left(\frac{x_i - \text{mean}}{\text{deviation}}\right)^3\right]$. But on the other hand a skewness…
Dan
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Proof that loss function for linear regression is an ellipsoid

I cannot seem to find a proof that $f(\mathbf{\beta}) = \left\lVert \mathbf{y}-\mathbf{X} \mathbf{\beta} \right\rVert^2$ is an ellipsoid, centered at the OLS solution $\hat{\beta}$. Can anyone show how to convert it to the quadratic form of a…
Presquevu
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If $X$ is exponentially distributed with parameter $1$, prove that $\exp(-X)$ is uniformly distributed on $[0,1]$.

This is what I have so far: The PDF of $X$ is $$f_X(x)=e^{-x}$$ when $x\geq0$ and $0$ otherwise. The CDF of $X$ is $$P(X\leq x)=F_X(x)=1-e^{-x}$$ when $x\geq 0$ and $0$ otherwise. I know that I want to end up with the pdf of $Y=e^{-X}$ being…
KaylaB
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Calculating the 4th number from 3 related numbers

I was taught a long time ago this really useful trick to calculate an unknown value when you know 3 existing values that are related. An example would be something like: If there are 21 peas in 3 pods how many are there in 17 pods? This gives us 2…
Jonathan
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Class Limits, boundaries, midpoint, relative frequency?

I have a…
m00nbeam360
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Why do we have to calculate 1-binomcdf for P(X>11)?

Why do we have to calculate 1-binomcdf for P(X>11)? Can't we just calculate binomcdf with left and right bound like the normalcdf?
WinstonCherf
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Kata's for Statistics

In programming one way at getting better at common problems is solving them in different ways with exercises known as 'kata'. I was wondering, since I'm long out of school, are there available exercises for statistics to increase ones math ability…
nobody
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