# Questions tagged [random-functions]

Functions of random variables.

157 questions
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### What simple function $f(i)$ produces an evenly distributed pseudorandom output for $i \in [1, 2, …)$?

I'm looking for a transformation $N \to S$ where $N$ is natural numbers sequence, whereas $S$ is an infinite pseudorandom sequence that doesn't end up with a repeating pattern and has a uniform ...
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### Can't understand finding characteristics of random variables

I have next random function as example in book: $X(t)=U*sh(t)-3e^{-3t}*V+t^2$ U and V - uncorrelated random variables. $U \in R(-3,3), V \in P(1,2)$. Next step is to find the characteristics of ...
1answer
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### summation of values of a uniform random variable

Say we have a random variable Y belonging to {-1,1}. Each time an ideal random number code-simulation generates a value for Y, using "Uniform distribution", let us give that value a symbol yi. So, ...
0answers
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### Random recursive function that stays near the initial value

I am working on a procedural CG scene and have populated a starry sky with particles of random size. My goal is to make the stars twinkle - in this case, by varying their size and/or alpha channels. ...
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1answer
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### A minimization chance constrained optimization problem

$\mathbf{Q}:$ Suppose we have the following chance constrained optimization problem: \begin{aligned} & \text{minimize} & & x_1 +x_2\\ & \text{s.t.} ...
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1answer
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### Sequence of Random Variables: Approximation to the probability of an event

i'd like some help with the following problem, please. Let there be a sequence of random variables $X_{n}$ such that $n\geq 0$. If $X_{n} \sim Beta (n,1)$ such that Beta distribution is ...
3answers
316 views

### Projections of uniformly distributed $\mathbb{R}^3$ unit vector have uniform distribution

My question revolves around the following property: Let ${\bf u} \in \mathbb{R}^3$ be a random vector with uniform distribution on the three-dimensional unit sphere. Then the projection on any given ...
2answers
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### Order Statistics and Functions of Random Variables

I'd like some help with following problem, please. $X \sim Bin(5; 0,2) \\ Y = \frac{1}{2}(Max(X,4) + Min(X,2))$ I need to find Y's density, but i don't really know how to apply Jacobian method or ...
0answers
53 views

### $X,Y \sim Exp(1), X \perp Y$, joint density of $V = X, U = X/Y$

I'd like to check if my results are correct. Could you guys please verify them? $X,Y \sim \; Exp(1), X \perp Y$ Find the joint density of $U = X, V = X/Y$: \begin{align} V = X/Y & \rightarrow ...
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### Does MCMC method can be used to calculate the mean and variance of the distribution of random variable functions?

I am not professional in Probability & Statisticsin, in order to clearly describe my problem, please be patient of the long introduction.THANKS! Background of my question Assume I have several ...