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Questions tagged [variance]

For questions regarding the variance of a random variable in probability, as well as the variance of a list or data in statistics.

In probability and statistics, variance is a measure of spread among the possible values of a random variable or a list of values.

More information can be found here.

2532 questions
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How to get this equation from the variance formula？

Let $X_1,...,X_n$ be an iid (independent and identically distributed) sample with mean $ \mu $ and variance $\sigma^2$. How to show $$ (n-1)S^2 = \sum_{i=1}^n (Xi-\overline X)^2 = \sum_{i=1}^n (Xi-\mu ) ^2 - n(\mu-\overline X) ^2 …
gong.y
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Help with a variance proof

I've been doing these exercises, but there is a proof (considering a binomial distribution of $n=4$, where $p$ is the probability of something happening, that has a median $m=4p$, prove, using the summation of $x_ip_i-m^2$, that the variance is…
Eduardo Vázquez Kuri
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Finding Cointegration

https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1404905. Hello everyone, In the link above, Meucci explains that in order to find a combination leading to cointegration of several series X , you have to find the vector w which minimise the…
JeanGuillaume
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Interpreting these given formulas...

I am writing a program for an assignment in which I need to incorporate these two formulas; but, the problem is, I have no understanding of the formatting of these formulas and I am just at a loss with what I could find online. Maybe the question I…
John Doe
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Is there a name for the function $\sqrt\frac{\sum (x - x^\prime)^2} {\sum x x^\prime}$?

Given two populations of ordered/named values, what (if any) is the name of the function given by: $\sqrt\frac{\sum (x - x^\prime)^2} {\sum x x^\prime}$ where $x$ is the value of a particular measurement in a given sample set and $x^\prime$ the the…
Bohemian
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How to find variance given mean and sum of square numbers?

A set of $20$ data values $\{x_1, x_2,\dots,x_{20}\}$ has $\sum\limits_{i=1}^{20} x_i^2 = 2872$ and $\mu=11$. Find the variance of the data set. The answer given is 22.6
John the User
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Are there two definitions of variance?

In some places the variance is defined as the sum of the squared differences of each data point value from the mean, divided the N - 1, and other places it's divided by N: Here The variance is the average number of these squared…
Zebrafish
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Variance of mean of set v. sum of variances of means of arbitrary partition of set

I'm interested in the relation between the variance of the mean of set of real numbers, $A$, and sum of the variances of the means of any arbitrary partition of $A$ into a smaller number of sets. Let's call the variance of the mean of the original…
num_39
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Textbook And ChatGPT Give Different Answers to Calculation of Variance, Which Method Is Correct?

I am learning A-Level Statistics together with my child and came across this problem: I then double-checked with ChatGPT, and it gave this answer: So who is right? Should we use Var(S) = $3^2$Var(S) as stated in the textbook, or Var(S) = 3*Var(S)…
Math_Physics
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The variance of the sum of $n$ random variables

becuase $$\left(\sum_{i=1}^n a_n\right)^2=\sum_{i=1}^n a_i^2 + 2\sum_{i=1}^n\sum_{j=1}^{i-1}a_ja_i$$ therefore $$\text{Var}\left(\sum_{i=1}^n{X}\right) = E\left\{ \sum_{i=1}^n [X_i-E(X_i)]^2 + 2\sum_{j=1}^n\sum_{k=1}^{j-1} [X_j-E(X_j)][X_k-E(X_k)]…
Ben
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Variance of Bernoulli random variables NOT independents.

Let $X,Y$ Bernoulli random variables with parameter $p$. My question is: Is it possible to cumpute the variance of $X+Y$ in the case when the variables are not independent?. My try…
Don P.
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Finding $\operatorname{Var}(X_{n})$ for some sequence of $X_{n}$

For sequence ${X_{n}}$ and ${Y_{n}}$, for each $n$, ${X_{n}}$ and ${Y_{n}} $share same distribution and they are independent. (think of ${Y_{n}}$ constructed in that way :independent.) $0 \le X_{n}$, $Y_{n}\le 1$ for all n. (${(1-X_{n+1})}$ /…
LANIOP
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Variance of sum of two dependent random variables

This question belongs to a problem set of MIT OCW probabilistic systems analysis and applied probability. Random variables X and Y have the joint PMF(probability mass function) P$_{X,Y}$ (x, y)=$\frac1 {72}$(x$^2$ + y$^2$), if x ∈ {1, 2, 4} and y ∈…
Ayush
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Calculate the variance of days of stock goes up

the price of a stock increases with the probability $1/3$, and decreases with probability $3/2$ daily. Let U be the number of days it goes up, after 5 days. What is $var(U)$? I think the expected value of U is 5 times 1/3 equals to 5/3, but I am…
Hanayozz
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Formula for conditional variance for continuous random variable.

I need to expand the conditional variance of continuous random variable as a sum of integrals. Here is my try: $$D(Y|X)=E[Y^2|X] - [E(Y|X)]^2 + EY = \int_y y^2f(x|y)dy -\left(\int_y yf(x|y)\right)^2dy $$ But I know that the second term is incorrect…
user
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