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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Distance distribution in different dimensions

This is a crosspost from this question on stackoverflow. It received no answers because "it is a math question". I don't know how to move so I crosspost. There are so many questions about distance distributions and the curse of dimensionality I did…
Sebastian
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method of moments poisson distribution not unique

We know that MOM estimate may not be unique. The most common example is Poisson distribution. From my lecture notes, it said if we only consider $m_1 = \mu_1'$, then we have $\hat{\lambda} = \bar{X}$. While if we consider $m_1 = \mu_1'$ and $m_2 =…
Jonathen
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Verifying a simple method to use $U(0,1)$ random generators with the CLT to sample from $N(0, 1)$

I am trying to understand an approach that was discussed in my pattern recognition class today of using uniform random variables, which can be sampled using some random generator, to obtain samples that are approximately $N(0,1)$. Unfortunately…
IntegrateThis
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Can mode lie between mean and median?

The distribution is left-skewed if meanmedian>mode. Can mode lie between mean and median?
eMathHelp
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Decreasing Sequence of Events in Statistics

There is a question from lecture notes whose answer I do not quite understand. The question is Let $X$ have a cdf $F$. Let $x$ be any point and suppose $x_n$ is a decreasing sequence such that $x_n \rightarrow x$ as $n \rightarrow \infty$. Show…
mathnoob
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Problem when calculating vaccine effectiveness

When calculating vaccine effectiveness against hospitalization from publicly available data, I came across a strange (mathematical) problem, which I do not know how to interpret. The problem occurs on real-world data, though for this question I…
xarx
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What exactly am I doing wrong in this problem?

There are two local factories that produce microwaves. Each microwave produced at factory A is defective with probability $.05$, whereas each one produced at factory B is defective with probability $.01$. Suppose you purchase two microwaves that…
Sarah
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Ordinal, nominal data type. what type of data is True/false matrix? (Level of measurement)

cat1 cat2 cat3 cat4 topic1 1 1 1 1 topic2 1 0 1 1 topic3 1 0 1 1 topic4 1 0 1 0 This data table means: When a topic belongs to category, the data entry…
user11656
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$\chi^2$ tests giving apparently conflicting results; and debate on validity of classical statistics

I've come across some very bright people who say that "classical statistics" is "plain wrong", as is also said about cosmology based on string theory. I think they prefer the "Bayesian" statistics that classical statistics replaced, or at least,…
Harry Macpherson
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What kind of calculations cause the sum of survey percentages to be greater than 100%?

I was looking at this Facts and Figures page for Mount San Antonio College and saw this note for the Age breakdown of the school: *note: Numbers do not add up to 100 because some students selected "unknown" or chose not to respond. This is the…
user391838
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Statistics question in cosmology

The following are the approximate parameters for the Benchmark model in cosmology: $H_0 = 73.8 km s^{-1} Mpc^{-1})$, $\Omega_{m,0} = 0.266$, and $\Omega_{\Lambda,0} = 0.734$. Given that we know $H_0$ very precisely to this value in a flat universe…
ObiDonKenobi
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Show $\frac{(n-1)S^2}{\theta}$ is pivotal quantity of random sample $Y_1,...,Y_n$ from $N(\theta,\theta)$ then derive confidence interval

Show $\frac{(n-1)S^2}{\theta}$ is pivotal quantity of random sample $Y_1,...,Y_n$ from $N(\theta,\theta)$ then derive confidence interval $(1-\alpha)100%$ confidence interval for $\theta$ So I can show that $\frac{(n-1)S^2}{\theta}\sim…
AColoredReptile
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How to Calculate a Weighted GPA

How would I be able to calculate my overall average grade (or grade point average) for these courses? Course Course Credit (weight) Course Grade Biology 101 45 86 Psychology 210 30 74 Chemistry 250 45 88 English 200 60 77 My…
Maldred
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Empirical Relationship between mean, median and mode.(Derivation)

How did we get the Empirical Formula? This formula has been etched into us in school but I want to know how this formula came about and to know if it's applicable for all statistical distributions or can only be used with large enough…
hawexrutile
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How do I calculate typical group size?

If I have a set of groups of individuals (e.g. people), and I want to calculate the typical group size (as observed by individuals), how do I do this? Wikipedia refers to this as "mean crowding" or "Typical Group Size" but doesn't give a formula:…
spookylukey
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