# Questions tagged [random-variable]

A random variable or stochastic variable is a value that is subject to chance variation (i.e., randomness in a mathematical sense).

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### Predict vector of random variables from historical data?

There's historical prices for gold, sp500, silver, iron. ...
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### Sum of two Von Mises random variables

I know that the sum of two independent normally distributed random variables is also a normal random variable, but is this true of other distributions? For example, what probability distribution does ...
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### Generate Multivariate Log-Normal Variables with given Covariance and Mean

Let ${\bf X}=(X_1,...,X_n)$ be an $n$-dimensional log-normal random variable. I want to $force$ my random variables to be such that $Cov(X_i,X_j)=\Sigma_{i,j}$ and $E(X_i)=\mu_i$ where $\Sigma_{i,j}$ ...
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### What is the purpose of doing Arithmetic(+-*/) on two different distribution?

I'm now learning mathematical-statistics, and I learned a lot of example, like " $X$and $Y$ are two independent gamma distribution, please prove that the addition of two gamma distribution is still ...
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### Are all ergodic random processes (at least wide sense) stationary?

If not, please provide a simple example of a non-stationary process that is ergodic (in mean and covariance).
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### How can I calculate Nagelkerke pseudo r2 with glmmkin object from GMMAT package in R?

I have used glmmkin function from GMMAT package to fit a logistic mixed model with the binary phenotype 'disease', one fixed variable 'PRS' and one kinship matrix 'GRM' to model the covariance ...
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### Expected wait time in two different types of banks?

Problem Statement There are two banks both have 100 people inside who want to cash their check and must do so by talking to the teller. In both banks, there are 10 tellers. In Bank 1 all 100 people ...
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### How to generate a vector that has zero correlation with another vector (in R)?

Suppose I have a vector v1 with values in the set {-1,0,1} ...
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### Finite $k$th moment of a function of random variable

Let $X = a/h$, where $X$, $a$ and $h$ are random variables, with $X$ an i.i.d. sequence. If $X$ has finite 8th moment, can we infer that $a$ has finite $8$th moment as well? Thanks
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### “Stable” distributions with integer support?

My understanding of stable distributions is that in order for a distribution to be stable, linear combinations of independent random variables from a given distribution (for example, a Gaussian) must ...
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### What are the conclusions to be drawn when a t-test is significant but a linear mixed effects model is not?

I have 30 participants. They have a pre score and a post score. I am testing whether this changes. There are five observations per participant. When the data are analyzed using a t-test there is a ...
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### Decomposition of auto correlated variable

Can the sum of two (or more) random variables with zero auto-correlations and zero cross-correlations yield a random variable that has non zero auto-correlation?
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### Variance of estimator of stratified sampling

Consider a stratified design composed of $H$ strata of size $N_h$, $h = 1, . . . ,H$. We want to estimate the population mean $μ_y$ of the characteristic $y$. Let $μ_{x,h}$ $h = 1, . . . ,H$ be ...