Questions tagged [random]

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

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5
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2answers
3k views

Connection to Normal distribution

I've been working on finding the probability for the event, that the sum of $n$ independent random variables are less than $s$, when they are evenly distributed on $[0,1)$. I've used the law of total ...
7
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2answers
652 views

How is a Halton sequence related to a Latin hypercube?

I currently use a Halton sequence to choose parameter sets for a prognostic model (e.g. using metabolic rate and protein content parameters to predict growth rate). From my understanding, both a ...
2
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3answers
1k views

How to compare randomness of two sets of data?

Given two sets of random numbers, is it possible to say that one set of random numbers has a greater degree of randomness when compared to the other? Or one set of numbers is more random when compared ...
15
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4answers
16k views

Sum of independent Binomial random variables with different probabilities

Suppose I have independent random variables $X_i$ which are distributed binomially via $$X_i \sim \mathrm{Bin}(n_i, p_i)$$. Are there relatively simple formulae or at least bounds for the ...
2
votes
2answers
1k views

What simple functions return equally distributed random values in an arbitrary given range?

For programming purposes I want a function f(x,R) that given a certain seed x returns the same random value every time, in an arbitrary range R. But, I also want the output to be equally distributed. ...
0
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2answers
104 views

Mapping between random strings?

Let us define a one-to-one function $f$ that maps binary strings of length $n$ to ternary strings of length $n$ such that if $x$ is random then $f(x)$ must be random. My question Is there an ...
1
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1answer
135 views

Shifting an LFSR loop in O(1) time?

I'm looking for a way to mathematically combine two concepts: LFSRs, and Barrel Shifters I'm looking for a way, in O(1) time, to shift an LFSR loop a given number of shifts. What I'm hoping to find ...
3
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0answers
139 views

LFSR with limited numbers of runs?

Is there a way to construct a linear feedback shift register (LFSR) which outputs no more than k consecutive 1s or 0s? (It would have to be not a maximal-length ...
25
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2answers
30k views

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]...
5
votes
1answer
278 views

Invertible $N \times N$ matrix over ${\rm GF}(2)$ having on each row and column $N/2$ ones

As per the title, I'm looking for the name and for a way to construct a ${\rm GF}(2)$ square matrix of size $N$ with the following properties: All rows/columns should be linearly independent On each ...
23
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4answers
18k views

uniform random point in triangle

Suppose you have an arbitrary triangle with vertices $A$, $B$, and $C$. This paper (section 4.2) says that you can generate a random point, $P$, uniformly from within triangle $ABC$ by the following ...
4
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4answers
5k views

Formula for Random

Since computers work off formulas, without greater knowledge one would assume that it would come up with the same answer for a set formula. However, you're able to tell it to generate a random number. ...
0
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1answer
2k views

Consequences of choice of a seed for random number generating algorithm?

Background I am trying to do a reproducible scientific analysis. My conclusions are not dependent on the random number generator, but the RNG does change the results ~1% between runs. I would like to ...
8
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2answers
9k views

Probability of Random number repeating

In the situation of having a high entropy random number generator, that generates numbers in the range of 0 and 2,147,000,000. If i have a list of 1,000,000 integer values, what are the chances that ...
1
vote
2answers
138 views

Are the values generated by non-linear equations truly random?

I was recently studying some literature on chaos theory and non-linear equations . where in various ciphers were created using non- linear equations like Lorenz equation . Are the data generated from ...
3
votes
1answer
985 views

Determining the period of a music player's “shuffle” feature

I ask this in a partly recreational, and partly research-related spirit, and I realize my problem might be ill-posed, so any suggestions for clarification might go a long way. Succinctly, my problem ...
3
votes
3answers
480 views

Deterministic random numbers generator using $p^n \mod q$

I figured that I can create a deterministic "random" numbers generator by utilizing a bit of "magic" that I picked up from some cryptography. However I seem to have missed a detail. Basically the ...
2
votes
3answers
599 views

Expected time of tree search algorithm on random input

We have a perfect binary tree on 2^k-1 nodes. Every node in the tree is marked with probability 1/2, and a node is either marked or unmarked. We want to find a marked node and return it. Our algorithm ...
1
vote
1answer
789 views

Proof for Minkowski reduced basis

I've read a few articles explaining the way to use the Minkowski reduced basis in a lattice in order to measure the uniformity of the output of a random number generator. However, I can't prove a ...
4
votes
1answer
1k views

Generalized Feedback Shift Registers

I find confusing some examples I have seen. Maybe you can help me to determine what is going on with them. A Generalized Feedback Shift Register (GFSR) sequence defines a sequence $\{W_{i}\}$ ...
3
votes
1answer
236 views

Max of multistep Gaussian walk vs max of multiple single-step Gaussian walks

Is there a relation between the max of a Gaussian random walk of 10 steps vs the max of 10 Gaussian random walks? Specifics (in Mathematica notation): ...
4
votes
1answer
2k views

Bays-Durham Shuffling

Reading "Random number generation and Monte Carlo methods" by James E. Gentle, I encountered an example concerning the Bays-Durham Shuffling algorithm whose result I can't reproduce. Basically, such ...
18
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4answers
1k views

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 ...
10
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3answers
3k views

The pseudoness of pseudorandom number generators

Is there a reasonable statistic test one can do to standard random number generators (say, one of those that come built in in Python libs) which shows they are not really random? (By reasonable I ...
5
votes
3answers
647 views

Polygonal billiards and uniform distribution

According to this article in Wikipedia: A billiard is a dynamical system in which a particle alternates between motion in a straight line and specular reflections from a boundary. When the particle ...
1
vote
1answer
475 views

Random assignment in blind experiments and “fair / just coin”

In blind experiments subjects are randomly assigned to one of groups. The most commonly used solution is to use (equivalent of) a coin toss, with the same probability to be assigned to each group. I ...
8
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2answers
1k views

Accessible Intro to Random Matrix Theory (RMT)

I read this fascinating article: http://www.newscientist.com/article/mg20627550.200-enter-the-matrix-the-deep-law-that-shapes-our-reality.html Unfortunately all the other papers I find googling are ...
11
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2answers
285 views

How can I randomly generate trees?

I want to randomly generate trees, i.e. undirected acyclic graphs with a single root, making sure that all possible trees with a fixed number of nodes n are equally likely.

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