# 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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### sum of two proportions

I have 10 sets of 100 marbles. I have two processes that pick marbles. One of them usually picks between 2 and 15% of the marbles in the set. Another picks between 0 and 90% of the marbles in the ...
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### Why condition on either the r.v. $X$ or $Y$ and integrate over a product of pdfs rather a single pdf to find this probability density?

Let $X$ have the probability density $f_{X}(x)=\lambda e^{-\lambda x}, \;\; x>0$ and let $Y$ have the probability density $f_{Y}(y)=\lambda e^{-\lambda x},\;\; y>0.$ Find the probability ...
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### Is it possible to have dependent and exchangeable random variables? [duplicate]

Is it possible to have dependent and exchangeable random variables? Someone told me yes.
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### Reciprocal of a binomial random variable

A production line produces faulty items independently at random with probability p. (a) Let X be the number of faulty items in a batch of 10. What is the distribution of X, and what is P(X = ...
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### Expectation and variance notation for ratio of random variables [duplicate]

When we have a ratio of random variables, is their expectation/variance defined in the same way? That is, if we want to write out explicitly $E[\frac{X}{Y}]$ where X and Y are random variables, then ...
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### Sample data and its corresponding random variables

Simple question but I can't find the logic behind that. In many texts I see expressions like "Let $\{ x_1, \dots, x_n\}$ denote our sample data and $\{ X_1, \dots, X_n\}$ their corresponding random ...
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### How to find the probability of a random variable being greater then another

So I have two independent random variables $X$ and $Y$, $Y$ ~ $U[0, 3]$ and the density function of $X$ is as follows: $f(x) = 1/3$ if $0\le x \le 1$ $f(x) = 2/3$ if $1\le x \le 2$ $f(x) = 0$ ...
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### Why do stochastic processes involve time? [duplicate]

We define random variables as functions on a sample space $X(ω), ω ∈ Ω$. Here I do not see time being involved. A stochastic process is a family of random variables, but they also are functions of ...
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### semi randomized order in k-fold cross validation with the R rminer package

I would like to conduct a k-fold cross-validation procedure (k=5) with the function "crossvaldata" from the R rminer package. However, I cannot divide the train and test sets into a completely random ...
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### Generate jointly distributed random coefficients with given mean and variance from $N(0,1)$ and some matrix $L$

Suppose $\beta_1 \sim N(m_1,s_1^2)$, $\beta_2 \sim N(m_2,s_2^2)$ and $cov(\beta_1,\beta_2) = s_{12}$. Now generate draws of these random coefficients from draws of two independent standard normal ...
### I have two sampling techniques $\varphi_1,\varphi_2$. Given $x=\varphi_1(u)$ can I compute a $v$ with $x=\varphi_2(v)$?
I have two sampling surjective techniques $\varphi_1,\varphi_2:[0,1)\to E$ mapping a random number $u\in[0,1)$ to a sample in a measurable space $(E,\mathcal E)$. Say $u\in[0,1)$ and $x:=\varphi_1(u)$...