Mathematics Stack Exchange
Mathematics Stack Exchange

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.

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generating sample from binomial distribution and calculate the mean and variance.

I am trying to calculate the mean and the variance from sample has generated from Binomial distribution .with p=0.1, m=number of trials is 100, n =sample size is 100 and N=nc 10^5.My equation is why the mean and variance sometimes are equal . M=V.…
salma
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Variance Calculation for Var(a + (b^2)Y)

What is $\mathsf{Var}(a + (b^2)Y)$ equal to? I understand that $\mathsf{Var}(aX + bY) = a^2\cdot \mathsf{Var}(X) + b^2\cdot \mathsf{Var}(Y) + 2(a\cdot b)\cdot\mathsf{Cov}(X, Y)$, but not sure how to calculate what $\mathsf{Var}(a + (b^2)Y)$ is…
user534867
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Why are there few formulas for variance?

I found few different formulas to calculate variance from different resources. I have searched the internet for quite a bit already and cannot understand why are they different. 1) $D(x) = \frac{\sum x_i^2}{n}-\bar{x}^2$ 2) $\sigma^2=\frac{\sum x^2…
Telion
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Is proving that $var[X_1+X_2]=var[X_1]+var[X_2]$ sufficient in proving $var(\sum\limits_{i=1}^n X_i $)=$\sum\limits_{i=1}^n var[X_i] $

Assuming $E[X_iX_j]=E[X_i]E[X_j]$ for i and j between 1 and n Is proving that $var[X_1+X_2]=var[X_1]+var[X_2]$ sufficient in proving var($\sum\limits_{i=1}^n X_i $)=$\sum\limits_{i=1}^n var[X_i] $. It seems pretty self-evident to me but perhaps do…
graphtheory
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Var(Y) orders of statistics

Problem regarding E[Y^2] $X$ is uniformly distributed in $[0,1]$, and $Y$ is uniformly distributed in $[0,X]$ (a) Find $\mathbb{E}(Y)$ and $\text{Var}(Y)$ Solution: By conditioning on $X$, we obtain the first two orders of statistics of $Y$ as …
useroe
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How to derive the variance of a point estimator that contains another estimator?

I am trying to derive an variance estimator $var(\hat{\theta}(\mu,x))$ for an point estimator $\hat{\theta}(\mu,x)$, where $\mu$ is the true mean, $x$ is the data. Now I need to replace the true mean $\mu$ with the sample mean $\hat{\mu}$. Then…
Vincent
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Variance of two random variables

I was given the following problem: The probability that a student drives a car, takes a bus, rides a bike or walks to school are 0.4, 0.2, 0.3 and 0.1 respectively. Suppose we randomly select 9 students and let $X_1$ be the number of students…
JoeyNYC
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Variance formula, $E^2(x)$ part

To find the variance for a variable I know you're supposed to use: $$Var(X)=E(X^2)-E^2(X)$$ When looking at the solutions to one of my class's problems I see $E(X)=p/(1-p)$. They then go on to say that $E^2(x)=p^2/(1-p^2)$. I'm confused because I…
MarksCode
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Variance of MLE $\sigma^2$ estimator

Let $X_1,X_2,\dots,X_n$ be an i.i.d. random sample from $N(\mu,σ^2)$. a. I found the estimator MLE of $\sigma^2$ $$\hat{\sigma^2}=\frac{1}{n}\sum_{i=1}^n (X_i-\overline{X})^2$$ But how to calculate: $$Var(\frac{1}{n}\sum_{i=1}^n…
alto de aitana
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Find the mean and the variance of a sum

Suppose Y_n is distributed (μ_n, σ^2), where the covariance between any pair (m, n) is 0.5*σ^2. Find the mean and the variance of B = sum(n=1 to N) of (k_n*Y_n), where the k_n (n=1 to N) are constants. --- Not sure whether this is correct, I tried…
TheAverageAnne
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Help in understanding a proof in descriptive statistics

So, I found this proof of the variance of a discrete uniform distribution on Wikipedia (https://en.wikibooks.org/wiki/Statistics/Distributions/Discrete_Uniform) and I'm having trouble understanding what exactly was done from line 6 to 7. Here's a…
daniels
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Weighting two variables based upon variance

I want to weight the two variables based on the amount of error. More the error lesser the weight I want to give. e.g My variables are the distance from the origin(0,0) to two points with a gaussian noise of (0 ,5m) . dist1 = 2.8m ,…
vicky
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Variance and Relation to Mean

I know that $Var(X)=E[(X-E(X))^2]$ if $E(X)=0$, then $Var(X)=E[X^2]$ do this equals to zero also ?
JenuRudan
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Variance and second moment

I am encountering times when Var(X) is interchanged with $E[X^2]$ where X is a random variable and in the cases where E[X] = 0 I see why that is: $Var(X) = E[X^2] - (E[X])^2$. But sometimes that is not the case, i.e. E[X] != 0. Would you mind…
fullofquestions
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variance uniqueness

I got a list of N integers (without repetition) below 50, which always sum the same (so the mean is also the same) as the following: [1,2,3, 10,20] , mean = 7.2 I can swap two numbers, and the mean will be 7.2 again: [1,2,3, 11,19] , mean =…
Ragnagard
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