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

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How many different random numbers can you generate between zero and infinity?

My theory is that you can't generate any random number between zero and infinity. But thats kind of unexpected because you can generate 100 different random numbers between 0 and 100 and 1000 ...
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0answers
15 views

Algorithms for generating a random $n$-element subset [on hold]

Please give me references where I can find algorithms for generating $n$ $(n <N)$ non-repeating pseudo-random integer numbers from the interval $[1;N]$. In other words, algorithms for generating a ...
3
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1answer
94 views

Rectangle randomly thrown on chessboard

) I'm an electrical engineer and having a tough problem with... math :) geometry and probability... Here's the problem : We have an infinite chessboard. Each square of the chessboard is of known ...
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1answer
66 views

Do you need true randomness to beat the two-envelope game?

A well-known (non-)paradox in probability involves a two-envelope game played between two players, $A$ and $B$: $A$ selects two distinct (real) numbers, $x$ and $y$, writing each one down on a card ...
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0answers
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When is a coupling ''natural''?

The definition of coupling is written below. In some articles, I found the term "natural coupling". When is a coupling said to be ''natural''? Definition of coupling between two random variables: Let ...
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3answers
72 views

How to scale a random integer in $[A,B]$ and produce a random integer in $[C,D]$

I know there are many methods to scale a number from range $[A,B]$ to a range $[C,D]$, and I've searched over and over the web. I've seen this math.SE thread. I need to scale a big number (signed ...
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1answer
41 views

Variance and Expected value of internet connection

I am working on a probability/statistics problem! The problem is as follows: Your internet connection is very poor. It constantly alternates between being functional for x minutes and being down for ...
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1answer
107 views

Fast method to pick unique random numbers?

In general, computer simulation involving random numbers (lets say to simulate a fair deck of playing cards so $1$ thru $52$) runs fast if you only pick a few cards. However, as you pick more and ...
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3answers
40 views

How to handle dice probability? ie, how much more likely would 3 six sided dice give a higher sum than 3 four sided dice?

I am playing at making my own table-top gaming system/rules and I wanted to have a better handle on how likely different dice combinations will give a higher result than one another. I know that a six ...
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2answers
81 views

How to find the probability mass function (PMF) of X and Expectation of X [closed]

Suppose that you have n switches (n > 1), and that the probability of any individual switch not working is p. You consider two strategies for testing the n switches: ā€¢ Strategy A: Test each switch ...
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2answers
45 views

What are some fast ways to generate random numbers?

Many programming languages come with a function to give random numbers. I wonder how they implement that. Also, assuming the language doesn't have a random function, is there a way to generate them ...
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2answers
22 views

Probability of n random numbers under a threshold

If we choose N random numbers between 0 and 1 (uniformly distributed), what is the probability that at least n will be under some threshold t? For example I want to know if I have a list of 1,000,000 ...
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1answer
11 views

A low-discrepancy or quasirandom series which would guarantee all value sequences

I am trying to find a type of quasi-random sequence which would guarantee that it could produce all possible sequences of values within the possible value range, while still producing random-seeming ...
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1answer
57 views

Mathematically what are random numbers?

One topic in mathematics and computer science that always confused me were random numbers. I tried searching for the exact meaning but it feels kind of abstract and incomplete. Mathematically random ...
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0answers
57 views

Conceptual Understanding of a Simple Random Process

I have a simple discrete time random process that with probability $0.5$ chooses a deterministic sequence so that $X(t) = -1$, for $t<1$ and $X(t) = +1$ for $t \geq 1$, similarly with probability ...
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1answer
19 views

Unranking pseudo-random values to produce uniform distribution over all permutations

Following this question (and answers) on SO. The problem is to find a method to produce an unranking of combinatorial objects in random order, but in such a way that all possible orderings are ...
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1answer
26 views

Series of random numbers on a continuous function

At one point, I read about a function used to generate random numbers that follow a continuous pattern. By this I mean random numbers that as a series is random, but in which items tend to be ...
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1answer
28 views

Random numbers within a range?

(Note: When I say "random" just assume I mean pseudo-random) I have heard that random numbers are generated using this method: $X_{n+1} = (a X_n + b)\, \textrm{mod}\, m$ Using the time as the seed. ...
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3answers
28 views

Creating random numbers matching mean and standard deviation

I know how to compute mean and standard deviation for a given probe. But how do I the opposite? Given is the wanted mean and standard deviation and I want to create the probes. In other words: What ...
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2answers
42 views

How to decide the randomness of a dataset by checking the prime numbers inside it?

So it is weekend! I am reading currently a book where I found this sentence: "71 percent of men said they had a 'good sense of direction'. Only 47 percent of women reported same thing.", and I thought ...
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1answer
65 views

Cross Power Spectral Density from Individual Power Spectral Densities

Let $X$ and $Y$ be two zero-mean, wide-sense stationary random processes. The power spectral density of a process is the Fourier transform of the process's auto-correlation function. The cross power ...
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1answer
18 views

Calucluating probability of randomness of number in given range

Ok. Here's a question I just read in a book relating to combinatorics and probability. I'm not able to make head and tail about how I should approach it, so here goes: You have a device that ...
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2answers
44 views

Distribution of a random measure is determined by the characteristic function

I ham trying to understand a proof from a book I am reading. It says the proof follows directly from the prior theorem and I just can't see that. Let $X$ be a random measure on a locally finite, ...
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1answer
29 views

Function (algorithm) for obtaining random number(s) from dice

I'm afraid I don't speak maths very well. I hope this question is sufficiently comprehensible and mathematical. Suppose I have a perfect D$x$ (i.e. $x$-sided) die, and a pen and paper, and with these ...
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1answer
53 views

Monte Carlo gamma function

This question was asked before but I'd like to ask something more precise given the answer that was given. [ Estimate gamma function using monte carlo ] What is the criterion for a random point to ...
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1answer
54 views

Can you generate math problems that are solveable?

If you take Linear Programming, it problems are formulated like this: You know that Cabinet X costs 10 cents per unit, requires 6 square feet of floor space, and holds 8 cubic feet of files. ...
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0answers
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Covariance of a random variable and its mean estimator

I was wondering if there is a common solution for the covariance of a random variable $x[n]$ (i.i.d) and its mean estimator $\hat{\theta}$. Mathematically, \begin{equation} \sigma^2 \left ( ...
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1answer
63 views

Solution for the Tall movie-watchers problem!

The question which I write is a changed format of what I have faced, in my project. I changed it to an attractive question and named it by "tall movie-watchers problem": Suppose that a small cinema ...
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0answers
22 views

Magnitudes of roots of random polynomials

I'm looking at the roots of random polynomials with integer coefficients, and constant term=leading term = 1. Using the Mathematica code ...
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1answer
72 views

Dividing gems by random permutation

A group of people have found a treasure of gems: $G=90$ green and $B=990000$ blue. They decided to divide it among them. Since there are more people then gems, they decide to order themselves in a ...
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1answer
35 views

Unexpected behavior with random numbers

I am trying to write a program dealing with random number generation, but I figured this would be the best forum to ask this. My program will, given each of the March Madness teams' probabilities of ...
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1answer
29 views

Random Shots and percentages behind it.

Just to be clear I am rather bad at math, however I am making a webservice and need to understand the math behind it in order to recreate it in javascript. So here goes.I am trying calculate the ...
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0answers
37 views

Covariance and correlation of summations of independent random variables

This is the problem: There are 2n āˆ’ 1 independent random variables X1, š‘‹2, ... , š‘‹2š‘›āˆ’1. The expectation E(Xi) is Ī¼ for all i = 1,...,2nāˆ’1. The variance Var(Xi) is Ļƒ2 for all i = 1,...,2nāˆ’1. Let ...
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Question about noise term in SDEs

Do any properties/assumptions of SDEs prevent the noise term from being extremely large? Using a simple population growth model as an example, $\frac{dNt}{dt} = (r_{t} + W_{t})Nt , N0$ given, ...
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2answers
102 views

Does randomness exist? [closed]

I've been plagued with this question for a few years now and wanted to know what others think. Does true randomness really exist? In mathematics, a random process is based on the concept of random ...
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0answers
13 views

Generate list of random items without dublicates

I need to generate list of random int items without duplicates. for example: n = 6( 0, 5, 2, 3, 1, 4). I write simple algorithm based on ...
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0answers
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Lyapunov exponents of dual / adjoint / transpose random dynamical system (RDS)

Consider the the state of a system at time $n$, $X_n$, as the action of a product of i.i.d. $d\times d$ random matrices acting on a $d$ dimensional vector $X_0$, so we have $$X_n = A_n \cdots ...
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1answer
52 views

Are there any Martin-Löf random reals that are computable?

For example, Chaitin's constant is both Martin-Lƶf random and uncomputable. Are there any examples of numbers that are Martin-Lƶf random but computable?
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Fourier transform of a real white noise on a 3D cubic lattice

I'm facing the following problem: I have a cubic domain of side $L=2\pi$; this domain is divided in a cubic grid, each side is divided in $N$ points, where $N$ is an even integer number. the ...
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Sum of random numbers and e constant [duplicate]

I recently came across this interesting fact: Take some (pseudo)random numbers between 0 and 1. Now sum this and count how many you need in order for their sum to be greater than 1. If you repeat ...
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1answer
16 views

What is the average minimum distance between two Sobol points?

Having the first n points of a d-dimensional Sobol sequence, what is the average Euclidean distance from one arbitrarily point to its nearest neighbour?
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1answer
28 views

Covariance of random variable as a function of distribution of noise

Consider the following stochastic difference equation \begin{equation} x(t+1) = x(t) + \nu(t+1) \end{equation} where, $x(t)\in\mathrm{R}$ be one dimensional and $\nu(t)$ be the disturbance with an ...
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2answers
121 views

Random directions on hemisphere oriented by an arbitrary vector

Hy, i'm writing a raytracer, and for that I need to generate n random vectors that are inside an hemisphere oriented by the surface normal. Ideally, I would also like being able to restrict the rays ...
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0answers
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Chi squared uniformity test for randomness

I'm evaluating some pseudorandom binary sequences, and I have a doubt. To begin with my reasoning was, let's apply a double tailed test to the chi squared statistic, because since I'm looking to see ...
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2answers
59 views

Probabilities seem to be growing exponentially

We have instituted random drug testing at our company. I was charged with writing the code to generate the weekly random list of employees. We've gotten some complaints because of people getting ...
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0answers
27 views

Method or Algorithm to produce near-accurate probability selection

Are there any known algorithms or methods to accurately identify, using random occurrences, the most probable next occurrence(s) as a pre-determined length of number set, by providing an already ...
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3answers
107 views

Uniformly Random Tuples

Consider a multiset of natural numbers. As an example take $$ M = \{1, 2, 2, 3, 3, 3\} $$ If we treat copies of the same number as indistinguishable, there are 8 distinct 2-tuples we can form from ...
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How to perform sampling using O(log n) random bits per sample irrespective of the values of pi?

I am not able to find a sampling for the following problem. "Consider a problem of using a source of unbiased random bits to generate samples from the set S = {0,1,...,n-1} such that the element 'i' ...
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1answer
13 views

hypergeometric distribution and random sampling

Is there any simple and fast algorithm (to be implemented in Javascript) to obtain a sample from the hypergeometric distribution? My needed sample size is very large (100,000,000).