# 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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### If a random variable is independent of two random variables separately, is it independent of them jointly? [duplicate]

Does the following rule hold? $\left\{ \begin{array}\\ X \perp Y \\ X \perp Z \end{array} \right. \Rightarrow X \perp Y,Z$ If it does not hold, what is a counterexample?
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### Random Variable Confusion

What is the difference between saying X is a random variable following normal distribution and X is normally distributed. Is the random variable implicit or is X in the second case some other entity?
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### How can you estimate the actual number of options when there is some "fuzziness" involved? (Valve check/parking tickets)

I received a parking ticket the other day. By checking the valve positions the parking company claim that my car hadn't moved for a certain period. The protocol from the valve check shows that the ...
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### Largest order statistics of non-identical distributions when extra information is available

Suppose we have two independent draws, one from a distribution $F_1$ and the other from a distribution $F_2$. The two distributions have the same support, say $[0, 1]$. The distribution of the largest ...
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### What is the distribution of the difference of two independent multinomial random variables?

Say I have two independent random vectors $X_c$ and $X_f$. The random vector $X_c$ is composed by three random variables: $X_{1c}$, $X_{2c}$ and $X_{3c}$. The second random vector $X_f$ is composed by ...
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### Expectation of number of voters who agrees with the proposed plan under the majority voting

This question raised in my research work and it is quite challenging for me. Consider a committee $D$ of $n$ voters, among these $n$ voters there are $n_1$ voters agreeing with the proposed plan, ...
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### Find the probability density function of $Y = X_1 + X_2$ [duplicate]

Suppose that $X_1$ and $X_2$ are i.i.d random variables and that each of them has a uniform distribution on the interval [0,1]. Find the probability density function $Y = X_1 + X_2$ I understand that ...
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### When you are running an analysis with only an intercept, does it make sense to include random subject and item intercepts?

Lets image a study where people get two shapes and are told to pick one. They each get 40 trials, each with a different shape/colour. There are 40 different pairs of shapes. There are 100 participants....
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### Transformation of Random variable

Suppose I have $N$ random variables $\{X_i\}_{i=1}^N$, and I want to calculate the expectation of a function of these random variables: \mathbb{E}[g(X_1,\cdots,X_N)h(X_1,\cdots,X_J)]=\int g(X_{1},\...
### How do I generate $n$ random variables that follow a correlation matrix with individually log normal distributions?
Short and sweet: I'd like to model $n$ random variables representing price changes of individual assets. Each of these should be distributed as a log normal variable with a median of 1. Is there a way ...