Mathematics Stack Exchange
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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.

37109 questions
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Percentage of risk, Is my calculation correct?

X is the worst scenario. In order for X to occur, two things must happen, in sequence. An event with an occurrence chance on 1/120 must occur. This is EVENT A. if EVENT A occurs, another event with a 2/100 occurrence chance must occur. This is…
JasonGenX
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Estimating word frequency for a set of texts

I have 37 files of different sizes, containing a total of 7 million words. I want to estimate the frequency of each word in the corpus. Let's say I find the word "Cranberry" only twice in the corpus, then it would be naive to state the frequency of…
user111322
  • 137
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Standard deviation of sample: why $n-1$ instead of $n$?

I'm trying to undertand why we use $n-1$ instead of $n$ while calculating the standard deviation of a sample. This site says that it is because $\sum{x_i-\overline{x}}=0$, and $\overline{x}$ is aready determined from before. Hence, the sample has…
user67803
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Is a probability in the $z$-table less than or less than and equal to the $z$- score?

When you look up the probability in a $z$-table is that the value less than or less than or equal? For example is it $p(z<2.35)=.0094$ or is it $p(z\leq2.35)=.0094$? And if they aren't equal then how would you calculate the other one? I would think…
SamFisher83
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IF $f(x)= \frac{1}{\mu} e^{-\frac{x}{\mu}} $ Write the likelihood function to find those observations.

Suppose a measurement process is applied to something whose actual value $\mu$ is given by the probability density function $f(x)= \frac{1}{\mu} e^{-\frac{x}{\mu}} $ Suppose we have observations $x_1, x_2 \ldots, x_n$ were taken with precision…
HUmbertto Ramso
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Problems with the definition of $R^2$

Wikipedia, defines $R^2$ or R-squared as follow: In statistics, the coefficient of determination, denoted $R^2$ or $r^2$ and pronounced "R squared", is the proportion of the variation in the dependent variable that is predictable from the…
Etemon
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most common subsets

Excuse the ignorance here. My background is not mathematics. This is an IT problem that may have a mathematical solution: I have a large amount of sets of variables. The variables belong to a distinct set of data (for example, each variable may be…
Dimitris
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Awkward question - pairing average for two different types of elements where ratio is 1:1

Not sure if this is adequate for math.stackexchange but please let me know and I will delete it. I've tried to make it more abstract, but then it would raise more questions than give answers. I've come across a statistic where it says that men have…
user85190
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Why is the expected value of Kolmogorov Smirnov statistic converges to 0?

Let $X_1,...,X_n$ be a random sample with distribution function $F$ and let $F_n$ be the corresponding empirical distribution function: $$F_n(x) = \frac{1}{n} \sum_{i=1}^{n}1_{(-\infty,x]}(X_i)$$ My book says that $\lim_{n->\infty}E(\sup_{x\in…
HHQ
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Significance of t-tests and outlieres

I was performing paired t-tests and came across the example from the R function. They show that addition of strong outlier can make the test more compliant about differences: t.test(1:10, y = c(7:20)) # P = .00001855 t.test(1:10, y = c(7:20,…
Renaud Bied-charreton
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Convergence in distribution of weighted average

Consider the following setting: $X_i\sim P_X$ iid for $i = 1,2,\dots, n_X$, where $P_X$ is a probability distribution with mean $\mu_X$ and variance $1$, $Y_i\sim P_Y$ iid for $i = 1,2,\dots, n_Y$, where $P_Y$ is a probability distribution with…
Quertiopler
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The logic of P values and rejecting

Could someone please explain the logic of the reasoning behind why we reject the $H_0$ if the $\alpha$ exceeds the $p$ value What I understand is that $\alpha$ is the probability of making a type 1 error if $H_0$ is true. $p$ value is the likelihood…
Ved Brahmbhatt
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When can standard deviation be equal to range

I was learning basic statistics and I read a proof that the standard deviation is always less than or equal to the range. I don't understand how range can ever be equal to the standard deviation. I could only think of one case: when all data points…
Mr.Curious
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Probability of student not taking course

An elementary school is offering 3 language classes: one in Spanish, one in French, and one in German. These classes are open to any of the 87 students in the school. There are 34 in the Spanish class, 31 in the French class, and 19 in the German…
papayaaa
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GLR test of hypothesis for exponential distributions

I'm having trouble with this exercise from Bain and Engelhardt's textbook: Consider independent random samples of size $n_1$ and $n_2$ from respective exponential distributions $X_i \sim EXP(\theta_1)$ and $Y_i \sim EXP(\theta_2)$. Derive the…
Camilo Acevedo.
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