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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First step in statistics: something-like-a-mode for a sequence where each value is different from another

Sorry but I'm not a statics expert at all, but I'm following some on line course and it is fascinating me. I just found the existence of the mode: The mode is the value that appears most often in a set of data. (Wikipedia) What about a sequence…
nkint
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What is $\left(\bigcup\limits_{n=1}^\infty E_n\right)^c$?

In an experiment, die is rolled continually until a 6 appears, at which point the experiment stops. What is the sample space of this experiment? The sample space consists of sequence where the last entry must be equal to six and no other entry can…
Username Unknown
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How to reduce the mean on a dataset without changing the order of the data

I created a list of anime I have completed and for each anime that I have completed I give it a score based on how good I thought it was. Now over time there are like 200+ anime in that list. But I now feel like my scores are very inflated. I want…
AllLuckBased
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Notation regarding a value corresponding to a particular rank

I have a hard time trying to come up with a formal way of writing the following problem. Basically I would like to find a value that corresponds to a certain rank (this certain rank might not be an integer). Here's an example: I have a vector of…
Code2Math
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the expected value is a non-negative random variable is always greater than the expected value of its subset?

Let's say $X$ is a non-negative random variable. And say $c$ is a positive constant. Why is $$E(X)\geq E\left(X_{\chi (X \geq c) }\right)$$ I don't know why the expected value is a non-negative random variable is always greater than the expected…
Jonathen
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How do a create a population given the mean, size and standard deviation?

How do I create a population (set of positive integers) given the size, mean and standard deviation? Like, if N = 7, mean is 50 and the standard deviation is 20, can I generate a population that fits that criteria?
username
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Calculating odds of Trading Cards

I'm trying to calculate the odds of a box of trading cards containing less than $100$ unique cards. From what I can gather, there's $11$ common cards per pack of $159$ unique common cards, $1$ item card of $13$, $1$ rare of $79$, one card that may…
WhatsANumber
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How to compare scores with different possible point totals

Is there way to fairly compare multiple scores with varying possible point totals such as 26/90, 54/70,67/80, etc...? This is based on the same test but not all questions apply to everyone taking it, so people don't lose or gain points if they are…
an2020
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Let $X_{1}, X_{2}, X_{3},...$ be a sequence of independent and identically distributed random variables, prove the following

Let $X_{1}, X_{2}, X_{3},...$ be a sequence of independent and identically distributed random variables with common (finite) mean $\mu$. Prove that there exists and event A such that $P(A) = 1$ and for all $w \in \Omega$, the quantity $\lim_{n \to…
user1070420
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Let $Z$ be a standard normal random variable, prove the following

Let $Z$ be a standard normal random variable, prove: $P(Z > z) \leq \frac{e^{-\frac{z^2}{2}}}{2}$ How do I approach this question? Do I assume the moment generating function (in Chernoff Bounds) is $e^{-\frac{z^2}{2}}$? Does it even have anything to…
sensationti
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Can we calculate the opponent's hidden values in this statistical battle?

First-order statistical battle Imagine there is a game in which the user should guess what values the opponent is hiding from the user. In the first battle, the opponent has two hidden values a and b where a is the mean and b is the standard…
Avestura
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Shifting functions to minimise the maximum variance accross a domain.

Assume we have a family of $N$ continuous functions $f_i(x)\in C_\infty$ along domain $D$. Define a set of constants $c_i \in \mathbb{R}$ and define the functions $g_i(x)$ so each $g_i(x)$. \begin{equation} g_i(x) = f_i(x) + c_i \end{equation} The…
Miro Astore
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Can the average of a set be lower than all of the averages of subsets?

Let's imagine there are marbles of different diameter and color. Can the average diameter of all the marbles be lower than all of the average diameter of marbles per color?
Auras
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Statistics percentage problem!

the english major at a university revealed the following: 10% failed math, 20% failed biology, 5% failed both math and biology. find prob: a) failed math, given he passed bio b) passed bio, given passed math c)passed math, known that he failed…
spiros
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For what reason are data sets with no repeating values defined as no mode whilst sets with n/2 is part of the set of integers is defined?

This question is in regards to the reasoning underpinning the definition of a set with no repeating values as having no mode. I am interested in the analytical philosophy behind this. A set with no repeating values is defined as having no mode. But…
duckegg
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