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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what am i doing wrong here? calculating standard deviation

I keep getting 2.02 for the standard deviation but the answer is 0.28? I'm not sure what I'm doing wrong, I even followed a step-by-step way to calculate it and I'm stilling get it wrong haha :^(
NookLines
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Is this an exponential distribution? (Variant of Gumbel distribution)

The distribution function is $$F_x(x\mid\lambda) = e^{-e^{-\lambda x}}, \qquad \lambda > 0$$ Is this an exponential family? The pdf that I obtained was $$f(x\mid\lambda) = \lambda e^{-\lambda x} e^{-e^{-\lambda x}}$$ and the joint pdf of an iid…
Ad22
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Should principles be proved?

I was wondering if one needed to prove principles. E.g., likelihood or condionality principles in Stats. Thank you!
Lola
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Moments based on a Bootstrapped Mean

Take $X_1,\ldots,X_n$ to be distinct observations, and let $X_1^*,\ldots,X_n^*$ be a bootstrapped sample (given a uniform resampling of cases with replacement) and let $\bar{X_n}^{*} = \frac{1}{n} \sum_{i=1}^n X_i^*$ (i.e. the mean of the…
Elaine
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Log likehood functions - Expected value

Let $X_1,X_2,\ldots,X_n$ be a random sample from a Bernoulli($θ$) distribution with probility function $$P(X=x)= (θ^x)(1-θ)^{1-x},\qquad x=0,1;\ 0 < θ < 1.$$ $dl/dθ = [n \overline{x}/θ] \cdot (n-n\overline{x})/(1-θ)$ <-- Is it this that's wrong? :/…
Fred
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Statistics Question

I'm revising for my exams and I want to check if I did this exercise correctly: 10 measurements were done using a certain tool. The average and standard deviations of measurements using a this tool are 0.4495 and 0.014 respectively. Test, using a 5%…
Sirzh
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Average volume of set of cubes using the mean and variance of its side lengths.

First, i tried this question: The side lengths of a set of squares have an average of 5 and variance of 4. What is their average area? Let X = The Side Length From this question , I knew we had to calculate $E(X^2)$. i.e. $$Var(X) = E(X^2) -…
Samy
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Does a factorable joint CDF/PDF always imply independence?

Say we have two random variables, x and y, with $F_{xy}(x,y)$ and $f_{xy}(x,y)$ denoting their joint CDF and PDF respectively. If they can be written such that $$F_{xy}(x,y)=G(x)H(y)$$ $$f_{xy}(x,y)=g(x)h(y)$$ is that enough to guarantee x and y are…
IPoiler
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What can Jensen's inequality tell me about bias of an estimator?

What can Jensen's inequality tell me about bias of an estimator? I don't really get how to use it and I would like someone to explain what convexity and Jensen's inequality has to do with bias. In particular, I am trying to learn to use Jensen's…
Stan Shunpike
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Mathematics of change money

Do you know any results or articles about change money? Something like the statistics of different value notes in a cash box. Or answers to questions which distribution of notes values is best for starting a day in a shop. I mean obviously you need…
Gere
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skew normal distribution

We have skew normal distribution with location $=0$, scale $=1$ and shape $=0$ then it is same as standard normal distribution with mean $0$ and variance $1$. But if we change the shape parameter say shape $=5$ then mean and variance also changes.…
user5620
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Should I round a R-Squared to fit with significant figures?

I have experimental data that I used to plot a calibration curve. If I have 2 significant figures in my data and a R-squared of 0.9959, is it correct to round the R-Squared to 1.0? How I think about it is that, since Excel must have used my data to…
Pierre-Éric
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How can I calculate this expected rate?

In DotA, there is a character called "Axe". Every time he is attacked, he has a chance to spin ($17\%$) his blade and deal damage based on what level the skill is, $100 / 125 / 150 / 175$ damage for levels $1, 2, 3$, and $4$. When the spin…
Jacob Greenleaf
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Central limit theorem, when do we know if n isn't large enough

I'm working on a statistics question, and I'm stumped on how to answer it. Here is the question According to a survey conducted by the American Bar Association, 1 in every 410 Americans is a lawyer, but 1 in every 64 residents of Washington, D.C.,…
user270494
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Alternative hypothesis when null hypothesis is ambiguous?

This is more of a textbook semantics issue. Is the alternative hypothesis always two-tailed when all that is known is a null hypothesis $H_0$ where $p$ equals some arbitrary figure, where an arbitrary sample proportion and significance level are…
mrtwj
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