Questions relating to (pseudo)randomness, random oracles, and stochastic processes.

# Questions tagged [random]

1726 questions

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### Difference between logarithm of an expectation value and expectation value of a logarithm

Assuming I have a always positive random variable $X$, $X \in \mathbb{R}$, $X > 0$. Then I am now interested in the difference between the following two expectation values:
$E \left[ \ln X \right]$
$\ln E \left[ X \right]$
Is one maybe always a…

Matthias

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### Expected time to convergence

Consider the following process: we place $n$ points labelled $1...n$ uniformly at random on the interval $[0,1]$. At each time step, two points $i, j$ are selected uniformly at random and $i$ updates its position to be a point chosen uniformly at…

michael

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### What is a formal definition of 'randomness'?

What is a rigorous mathematical/logical definition of 'randomness'? Under what conditions can we truthfully apply the predicate 'is random'?

duskn

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### 'normally distributed random numbers' vs 'uniformly distributed random number'?

what is the difference between 'normally distributed random numbers' and 'uniformly distributed random number'? A answer in a layman language is appreciated :)

user3130920

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### Is it possible to generate truly random numbers using a computer?

I know that there are many algorithms to generate pseudorandom numbers but is it possible to generate truly random numbers using a computer program?

Razin

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### 3 random numbers to describe point on a sphere

I'm currently working on a problem involving computer graphics and got into a discussion about whatever or not constructing a 3d vector out of 3 random points uniformly distributed points between -1 and 1 (and then normalize the vector) to get…

Thijser

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### So what really is a random variable?

I've been confused about the definition of a stochastic (random) variable for an embarrassingly long amount of time.
From the Wikipedia entry on Stochastic Processes, I could gather that a random variable is a map from a probability space…

user67803

**20**

votes

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### Summing (0,1) uniform random variables up to 1

Possible Duplicate:
choose a random number between 0 and 1 and record its value. and keep doing it until the sum of the numbers exceeds 1. how many tries?
So I'm reading a book about simulation, and in one of the chapters about random numbers…

Haile

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### Average norm of a N-dimensional vector given by a normal distribution

I'm interested in knowing what is the expected value of the norm of a vector obtained from a gaussian distribution in function of the number of dimensions $N$ and $\sigma$, i.e:
$$E[\|x\|_2],\quad x\sim\mathcal{N}(0,\sigma I_N)$$
I tried to search…

jmacedo

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### Powers of random matrices

Let $M$ be an $n \times n$ matrix whose elements are random reals in [0,1].
Two questions.
What is the growth rate of the magnitude of the elements of $M^k$ as a function of $k$? It is definitely
exponential, but maybe the exponent is known?
Is…

Joseph O'Rourke

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### Choosing two random numbers in $(0,1)$ what is the probability that sum of them is more than $1$?

Choosing two random numbers in $(0,1)$ what is the probability that sum of them is more than $1$?
Also what is probability of sum of them being less than $1$?
I think the answer should be $\frac{1}{2}$, but I have no idea.
EDIT: I should mention…

PLuS

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### Apparent Paradox in the Idea of Random Numbers

This question is a bit less than rigorous, but it's only because I don't know how to formulate it rigorously.
Suppose there was some machine, or function, or whatever that could output a random positive whole number. Let's say that it has done its…

Colin

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### what's the difference between RDE and SDE?

what's the difference between random differential equation and stochastic differential equation?
does stochastic differential equations include random differential equation?

Jim

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### Is there a "most random" state in Rubik's cube?

Is there a state in Rubik's cube which can be considered to have the highest degree of randomness (maximum entropy?) asssuming that the solved Rubik's cube has the lowest?

kunjan kshetri

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### How can I pick a random point on the surface of a sphere with equal distribution?

I've got a random number generator that yields values between 0 and 1, and I'd like to use it to select a random point on the surface of a sphere where all points on the sphere are equally likely.
Selecting the longitude is easy as all lines of…

billpg

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