# 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.

1,174 questions
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### Barttletts test and F test with 3 variables

I linked a picture with the assignment. I know how to do F-tests with 2 variances and means, but with 3, I am out of luck. I could do it if I had a dataset in R. but not manual in R or by hand, as it ...
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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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### Given $E[X] , \operatorname{Var}(X)$ and $Y\mid X \sim U(X,1)$, find $E[Y]$ and $\operatorname{Var}(Y)$

For $X, Y$ random variables, given $E[X] = \mu$ ; $\operatorname{Var}(X) = \sigma^2$; $Y\mid X \sim \text{Unif}(X,1)$: Find $E[Y]$ and $\operatorname{Var}(Y)$. (1) To find E[Y], I used the law of ...
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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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### Conceptual Understanding of Rate / Volume Analysis for Balance Sheet changes

Not sure if this is the right place to ask this but I searched and didn't find this question already asked. I am having a lot of trouble conceptually understanding the formulas behind a rate / volume ...
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### Minimum mean squared error of an estimator of the variance of the normal distribution

I am trying to find the estimator of the variance $\sigma^2$ of a normal distribution with the minimum mean square error. From reading up, I know the unbiased estimator of the variance of a Guassian ...
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### Probability- 6 digit number that is built from the numbers 2,5,6,9

A random 6 digit number is picked that is built only from the numbers $2, 5, 6, 9.$ What is the probability that the number can be divided by $3$? What is the probability that the number can be ...
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### Measuring the uniformity or closeness of a set of given values

Say we have a sample space of size $N$ . What's a good way to measure how close the values are to one another? In other words, to what degree are the values 'equal' to one another? I thought of a ...
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### Find covariance matrix of $\frac{f(x + y) }{x + y}$ function

The conditions are the same, but my task is to find covariance matrix. I only noticed that density function is symmetric so expected values, variance are also the same. But I don't know how to find ...
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### Calculating Variance(X + Y + 1)

Not Duplicate. I know a question with similar data has been used here, but I am looking for something else. Two tire-quality experts examine stacks of tires and assign a quality rating to each tire ...
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### $Var(\frac{1}{nh^d}\sum_{i=1}^n Z_i)=\frac{1}{n}E\bigg[\big(\sum_{i=1}^n Z_i-E(Z_i)\big)^2\bigg]$

Let $\{Y_i,X_i\} \in \mathbb{R}\times\mathbb{R}^d$ be a strictly stationary sequence of random vectors and consider $\hat{\Psi}(x)=\frac{1}{nh^d}\sum_{i=1}^nY_iK(\frac{x-X_i}{h})$, where $h=o(1)$ is ...
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### Sequence of independent random variables with same expected value such that the weak law doesn't hold

I'm looking for a specific counterexample for the weak law of large numbers. That is, I want a sequence of random variables with same finite expected value $\mu$. These random variables must each have ...
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### Standard deviation transformation sd(X-Y)

just need some help in this statistics question regarding the transformation of standard deviations. This is the question: Let R be the visual acuity readings for the right eye of a randomly ...
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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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### 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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### How to determine the variance of this Bayesian linear regression model

I am struggling with the following problem. I have a Linear regression model which uses bayesian statistics: $X_7 = X\beta + \epsilon$. Here $X = (X_0,X_1,...,X_6)$ is a data frame containing 7 ...
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my task is this: Be $X$ and $Z$ independent with the same distribution and $Y :=X-Z .$ Calculate $\operatorname{cov}(X, Y)$ and $\operatorname{corr}(X, Y) .$ My Problem is the minus in $... 1answer 37 views ### How to calculate E[Xi Xj]? This question is from an example in the book of Bertsekas. (p240 of 1st edition). I would like to know why $$E[X_{i} X_{j}] = P(X_{i} = 1\text{ and }X_{j}=1)$$ and $$E[X_{i}] = P(X_{i}=1)$$. please ... 1answer 16 views ### Law of total variance and covariance given X and Y are normal I have a problem which asks me to find$\Bbb E[Y]$and$Var(Y)$given that$Y\text{~}Normal(x,1)$conditional on$X=x$.$X$is standard normal. So I have worked out that$\Bbb E[Y]=0$using the law of ... 1answer 14 views ### Variance of inverse gamma distribution Given a random variable$X$which is distributed gamma with shape$\alpha$and rate$\lambda$, for which the variance is known, how does one calculate$\text{Var}(\frac{1}{X})$? I am hoping not to ... 1answer 23 views ### DEMONSTRATION FINITE-SAMPLE PROPERTIES OF LEAST SQUARES$\frac{(N-k)S^2}{\sigma^2}\sim\chi^2[n-K]$Im a Student of Economics, and I have a concern. In the solution of$\frac{(n-K)S^2}{\sigma^2}\sim\chi^2[n-K]$How can I show that if the matrix is ​​symmetric and idempotent between$(I-H)=|| (I-...
I have two random variables $$X_{s+t} \sim N(0, s+t)$$ $$X_s \sim N(0, s)$$ where $s \leq t$. How do I show that... $$X_{s+t} - X_s \sim N\left(0,s + t + s -2\sqrt{s(s+t)} \right)??$$ I understand ...