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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Given probability of A not B and probability of B not A, what is probability of A occurring before B?

Context: In a game I sometimes play, players roll percentile dice against one another to win points. Each player has a unique threshold they have to roll below to score a point, but if both players roll below their threshold, neither scores a point…
Koala4628
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celebrated Lindeberg condition

Lindeberg-Feller CLT is Theorem 4.12 in Foundations of Modern Probability by Olav Kallenberg that says Let $ (ξn,j;j=1,…,n)^∞_{n=1}$ be a triangular array of row-wise independent random variables with mean $ 0$ and $\sum_{j=1}^n…
kodar
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Statistical test for significance with categorical variables

Given a dataset of n records, each record having two attributes A1 and A2. A1 can be one of two categories: X or Y. A2 can be one of 10 categories, C1 to C10. Given the following hypothesis: If A1 is X, then A2 is statistically significant mostly …
partikel
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Derivation of the formula for the degrees of freedom for $\chi^2$

I am trying to understnad where this formula comes from: My first guess was that it has something to do with dimensions of subspaces, since for a goodness of fit test there is a system of equations "hidden" in a contingency table, I think. I found…
Hans
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How do you know when a question requires the use of the law of total probability?

This pertains to the following post: When to use Total Probability Rule and Bayes' Theorem. I understand the ideas and can implement them if I'm told what B and the partitions A are in the question - or that i'm meant to use the law of total prob -…
jm007
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Estimation of shape area given random points inside it

I have a shape $S$ of area $A$, but I do not know what $A$ is. However, I do have the coordinates of $N$ points (the coords are $(x_i,y_i)$ for $i\in[1,N]$) that follow a sampling distribution $D$. The probability density of $D$ is $0$ on points not…
Shiran Yuan
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Calculating SST only knowing the SSE and nothing else.

I have been given a problem in which I am asked to calculate the SST of $Y$ while only being given the SSE of each model (there are $3$ variables, $X_1 ,X_2 ,X_3$ and I have been given the SSE of all possible models that can be created with these…
Petros Xristodoulou
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Can credit card pin numbers be described as Qualitative - Ordinal?

I've just started taking statistics. Today the class was asked what type of data are credit card pins. The lecture leading up to the question gave us the following: Data can be described as being quantitative or qualitative. If qualitative, it can…
roundar
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Simplified formula for standard deviation does not work

I was given the following sample {9,8 ; 10,2 ; 10,4 ; 9,8 ; 10 ; 10,2 ; 9,6}. So if I compute the mean I obtain 10. If I compute the standard deviation with: $\sqrt{\frac{1}{6} \sum{(x_i-10)^2}}$ I obtain 0,2828. But if first I compute the mean of…
tac
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Statistics - Fine-grained data Generalization

I have a suspicion that I hope to get help in proving or disproving. I am either right or wrong, either is acceptable. I assert that gathering data, to be generalized later, can be gathered in too fine of detail and will produce or encourage the…
kalisjoshua
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For a given mode and median, maximum number of rejected pistons

A hydraulic cylinder manufacturing company has decided to outsource the surface hardening process of piston rods to one of the five shortlisted heat treatment companies. Each company has been given 100 piston rods for surface hardening, and any rod…
Vikas Sharma
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Sum of a set of numbers squared is larger than $N$ times the mean squared

I require the proof for the following $$\sum_{i = 1}^N x_i^2 \ge N \mu ^2 $$ where $x_i \in \mathbb R$ and $$\mu = \frac{1}{N} \sum_{i = 1}^N x_i$$ I can visually see how this is true (I imagine rectangles and squares), and would like to know if…
B2VSi
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Variance stabilizing transformation

I ran into this statistics question: In many cases, an estimator $T_n$ for $\theta$ is asymptotically normal distributed, but its asymptotic variance depends on $\theta$: $\sqrt{n}(T_n - \theta) \to N(0; \sigma^2(\theta))$ in distribution. It can be…
Leo
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What is estimated variance of a group mean?

Given that the totals of six values in each of $5$ groups are $360,246,420,336,306$ and the estimated variance of a group mean is $6.2$ ,compute the analysis of variance. I am not understanding only the fact that "What is estimated variance of a…
ABC
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When the distribution is negatively skewed, how do you find the probability that a sample would be less than ___?

I think my question has a really simple answer, but I’d still really appreciate your help :) I’m given that a distribution is negatively skewed with a mean of 55 and a variance of 15, and then am asked: for a random sample of n=80, what is the…
Iplaysoccer
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