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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100 people with 100 dollars each, give 1 dollar to a random other person. What's the distribution?

Source: http://www.decisionsciencenews.com/2017/06/19/counterintuitive-problem-everyone-room-keeps-giving-dollars-random-others-youll-never-guess-happens-next/ "Imagine a room full of 100 people with 100 dollars each. With every tick of the clock,…
Yashmnash
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How to find the covariance of sample mean and sample variance $Cov(M,S^2)$ for Poisson distribution?

Suppose that I have a Poisson distribution $P(\lambda)$. Let $X_1,X_2,\ldots,X_n$ be independent random variables from the distribution mentioned above. Let us define sample variance $S^2 = \frac{1}{n-1} \sum (X_i - M)^2 $ and sample mean as $M =…
Andrey Rubshtein
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How do I calculate a weighted average from two averages?

I have two sets of averaged data I am working with, which account for a score and the average amount of users that achieved this. For example: Average Score $4$, Total Number of participants (which the average is derived from): $835$ Average Score…
Hemmed
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Can kurtosis measure peakedness?

Wikipedia says kurtosis only measures tailedness but not peakedness. But I remember my teacher said several times that high excess kurtosis usually corresponds to fat tails AND thin peak. High excess kurtosis accompanied by fat tails can be easily…
Hank
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What does it mean when a statistician says I’m 90% confident that the mean of the population is between 1 and 9?

Does that mean if I draw samples from the population that 90% of the time I'll get a number between 1 and 9? Added: assume normal distribution for the population.
user133466
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Confidence interval for uniform

A random variable is uniformly distributed over $(0,\theta)$. The maximum of a random sample of $n$, call $y_n$ is sufficient for $\theta$ and it is also the maximum likelihood estimator. Show also that a $100\gamma\%$ confidence interval for…
adamG
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What is the relationship betweeen a pdf and cdf?

I am learning stats. On page 20, my book, All of Statistics 1e, defines a CDF as function that maps x to the probability that a random variable, X, is less than x. $F_{x}(x) = P(X\leq x)$ On page 23 it gives a function $P(a < X < b ) =…
bernie2436
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What does -1.13 times faster mean?

I'm reading High Performance JavaScript, and I think the graphs in one chapter are just plain wrong. Here is one on Google Books. The y axis is "Times faster", and it runs from -1.5 to +4.0. Now, I would have thought that "1 times faster" means "no…
Skilldrick
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Does Variance depend on change of scale and origin?

I know that SD depends on change of scale and not on change of origin. But what about Variance? And why?
Fred
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Intuitive explanation for dividing by n-1 when calculating sample variance?

I understand how to mathematically show that the sample variance (that involves dividing by n-1) is an unbiased estimator of the population variance (which divides by n), and the mathematics has been shown many times here on Math.SE. I am wondering…
Kenshin
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Problem with unbiased but not consistent estimator

I have some troubles with understanding of this explanation taken from wikipedia: "An estimator can be unbiased but not consistent. For example, for an iid sample $\{x _1,..., x_n\}$ one can use $T(X) = x_1$ as the estimator of the mean $E[x]$.…
Darqer
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Confidence interval multiplication

The question looks pretty simple but I can't get my hands on it: Say I have a probability which is the product of two other independent probabilities $p = p_1p_2$. I have estimated each probability $p_1$ and $p_2$ and found some $95\%$ confidence…
user88595
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Explanation for the Wilson Score Interval?

I'm looking at this blog to try to understand the Wilson Score interval. I understand it somewhat, but I'm confused by the part under the title "Excerpt". In particular, I don't understand what he's calling the "Interval equality principal" and how…
u3l
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Same mean, different standard deviation in data sets

How would a data set containing the values of a variable with a mean of 50 and a standard deviation of 3 compare with another data set containing the same variable, but a mean of 50 and a standard deviation of 12?
Faye
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A value has 'reduced by factor of 3'. Does this make mathematical sense?

I'm just reading some statistics. Last year there were 3000 observations, this year there are only 1000. This is described as showing a "fall by a factor of 3". This phrase doesn't ring true. If a factor of 3 is a 1/3, then a fall by a third would…
ianmayo
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