# 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.

451 questions
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### Seemingly Identical Random Variables with Different Variances

In my probability class, we did the following problem regarding expected values/variance: Consider an experiment where you roll a fair, 6-sided dice until you see a 6. Let $T$ be a random variable ...
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### Let $s^2=\frac{1}{n}\sum_1^n( X_i-\bar{X})^2$ and $\widetilde{X}$ denote the sample median. Is $s^2\leq \widetilde{X}(1-\widetilde{X})$ true

$X_i\in[0,1]$ Let $s^2=\frac{1}{n}\sum_1^n( X_i-\bar{X})^2$ and $\widetilde{X}$ denote the sample median. Is the following true? $$s^2\leq \widetilde{X}(1-\widetilde{X})$$ I couldn't find any ...
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### Brownian Motion and Variance

If $(W_t) _t$ is a Brownian motion regarding to a filtration $(F_t) _t$ and the process $Z(t)$ is defined by $$Z_t= \int_0^t W_s ds$$ What is $\operatorname{Var}(Z_t)$?
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### The joint density of X and Y is given by…

The joint density of $X$ and $Y$ is given by $$f_{X,Y}(x,y)= \left\{\begin{matrix}(x+y), \mbox{ } 0\leq x \leq1 , 0\leq y \leq1 \\ 0, \mbox{ otherwise}\end{matrix}\right.$$ a) Evaluate $f_{X}(X)$ ...
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### Variance estimation question and unbiasedness.

Hello I have a problem with variance estimation for RQMC. I have $\{x_1,...,x_n\}$ Sobol points. A randomised set $\tilde{\mathfrak{X}}$ is generated by the random variable $\epsilon$. For a ...
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### Variance service times M/G/c queue

I am wondering about the influence of the variance of the service times in an M/G/c queue on the probability that a customer has to wait. Intuitively, I would say that smaller variance implies smaller ...
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### Calculate p-value between two lists of floats of unequal size

I would like to calculate the degree of variance between to lists of floats of unequal size expressed in a p-value. I tried a two-sided t-test as in the example below using python. But answers that ...
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### Which is faster: a bank with five lines of ten or one line of fifty?

I'm working on a probability question with mean and variance. Let's say that I have two banks. They are identical in every way, except that bank A has five lines with ten people and bank B has ...
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### Value At Risk Elliptical Distributions

I thought I understood elliptical distributions, but then I staggered over the following problem: Let d financial returns be modeled as the components $X_1,...X_d$ of a d-dimensional random vector $X$...
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### Sum of exponential series of equal mean and variance

Assuming $A$ and $B$ are two non-negative real-valued random variables such that $\mathrm{E}(A)=\mathrm{E}(B)$ (equal means) $\mathrm{Var}(A)=\mathrm{Var}(B)<\epsilon$ (equal small variances) is ...
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### Distribution/Variance of correlated squared normal random variables

If $X_{1}, X_{2}, \ldots, X_{N}$ are identically distributed normal random variables with mean $0$ and variance $\frac{(N+3)D\sigma^{2}}{N}$, then I want to calculate the distribution, or at least the ...
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### Linear regression and constant conditional variance

This is an exercise found in Mathematical Statistics with Applications, by Freund. The book defines the regression equation of $Y$ on $X$ as $$\mu_{Y|x} = E[Y|x] = \int_{-\infty}^{\infty}yf(x|y)dy$$...
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### Variance of limiting distribution equal to limit of variance

I have a possibly basic question, which I am not sure on whether or not it is true. Suppose we have a sequence of identically distributed, but not necessarily independent random variables $X_n$ on a ...
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### Calculate covariance given correlation, problem with percentages

The question is: find the covariance of ABC stock returns with the original portfolio returns. Pretty straightforward. However I get confused working between percentages and units. The ...
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Let $\{Y_{i}\}_{i=1}^{n}$ be a random sample of the random variable $Y_{i}\sim \mathcal{N}(0,\sigma^{2})$, we define the following estimators for $\sigma^{2}$ $U=\frac{1}{n-1}\sum_{i=1}^{n}(Y_{i}-... 0answers 17 views ### Connection between$\operatorname{Var}(M^n v)$and largest eigenvalue of$M$In a proof I am trying to understand, the following is stated:$ M$is a non-random matrix with eigenvalues$\lambda_i$,$v$is a random vector,$n$is a scalar,$\operatorname{Var}(M^n v) \ge \max(|...
I have reached to $\mathbb{E}[\|x_tx_t^T - G_t\|^2_F]$, and I need an upperbound for it in terms of probabilistic characteristics of $x_t$ where: $x_t$ is a random vector in $\mathbb{R}^n$ drawn from ...