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

learn more… | top users | synonyms

4
votes
1answer
93 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 ...
1
vote
0answers
71 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 ...
0
votes
1answer
34 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 ...
0
votes
1answer
34 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 ...
0
votes
1answer
60 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. ...
0
votes
3answers
50 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 ...
0
votes
2answers
70 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 ...
2
votes
1answer
112 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 ...
0
votes
1answer
24 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 ...
1
vote
2answers
54 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, ...
1
vote
1answer
124 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 ...
1
vote
1answer
74 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 ...
1
vote
1answer
68 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. ...
0
votes
0answers
13 views

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 ( ...
0
votes
1answer
64 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 ...
3
votes
0answers
26 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 ...
1
vote
1answer
74 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 ...
0
votes
1answer
41 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 ...
0
votes
1answer
43 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 ...
0
votes
0answers
52 views

Covariance and correlation of summations of independent random variables

This is the problem: There are 2n − 1 independent random variables X1, 𝑋2, ... , 𝑋2𝑛−1. The expectation E(Xi) is μ for all i = 1,...,2n−1. The variance Var(Xi) is σ2 for all i = 1,...,2n−1. Let ...
0
votes
0answers
42 views

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, ...
4
votes
2answers
123 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 ...
0
votes
0answers
25 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 ...
1
vote
0answers
33 views

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 ...
2
votes
1answer
65 views

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

For example, Chaitin's constant is both Martin-Löf random and uncomputable. Are there any examples of numbers that are Martin-Löf random but computable?
1
vote
0answers
26 views

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 ...
1
vote
0answers
30 views

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 ...
0
votes
1answer
23 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?
0
votes
1answer
36 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 ...
1
vote
2answers
301 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 ...
0
votes
0answers
29 views

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 ...
1
vote
2answers
62 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 ...
0
votes
0answers
43 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 ...
8
votes
3answers
135 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 ...
1
vote
0answers
42 views

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' ...
0
votes
1answer
17 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).
0
votes
0answers
43 views

Expectation of a convolution between a WSS random process and an LTI system

Let $X(t)$ be a wide sense stationary random process―i.e., its expectation is a constant and its autocorrelaton function is a function only of time differences―and let $Y(t) = X(t) * h(t)$ where ...
8
votes
3answers
878 views

How can one create random numbers with special correlations?

Is it possible to create uniformly distributed real pseudo random numbers $x_1,x_2$, and $y_1,y_2,y_3\in$ $[0,1]$, subject to the following constraints: $$x_1^2+x_2^2=1$$ $$y_1^2+y_2^2+y_3^2=1$$ I ...
2
votes
0answers
17 views

spectral norm of a sparse Gaussian matrix

Suppose $G$ is an $m \times n$ matrix such that each entry of $G$ is a standard normal variable. We know that the spectral norm of $G$ scales as $\sqrt(m) + \sqrt(n)$. Now, given a set of indices $S$ ...
0
votes
1answer
49 views

Given a list of integers between $0$ and $99$, create a function that will fit all the integers in the list.

Okay, so my friend LOVES to play the lottery. He makes bets often with bookies on the last $2$ digits, getting $90:1$ on his money, a losing bet. He looks up 'systems' on social media on how to ...
0
votes
1answer
29 views

Multiple rolls of a one hundreded sided dice

Let's side I have a one hundred sided dice and a friend picks 8 random numbers from the dice. I understand that if I roll the dice one time, he has an 8% chance of getting the roll correct. My ...
-2
votes
1answer
27 views

is it possible to implement random(0,1,..,m) with finite calls to random(0,1)? [closed]

that is, is there a function $f$ that $Y=f(m,X_1,X_2,...,X_{n(m)})$ where $X_i\sim B(1,\frac{1}{2})$ and $Y\sim U\{0,m\}$? e.g. when $m=2^k-1$,$n(m)=k$ and ...
2
votes
1answer
25 views

Random allocation of groups of objects to agents

I have a poorly specified random allocation problem, which I need help in trying to tighten the definition and consider an effective algorithm. I have groups of objects, each group containing at ...
0
votes
0answers
15 views

K-Uniformity of Infinite Sequence

A book on random number generators refers to the subject of infinite-uniform infinite sequences as being "random." I was wondering if anyone could shed light on the definition of K-Uniform Infinite ...
1
vote
2answers
107 views

Probability that an individual cheated and knows a random sequence.

Bob writes down a sequence of coin flips on a piece of paper and hides it away. He uses a coin flip to determine if he uses a 1 or a 0. Alice tries to guess the random sequence and may have looked at ...
0
votes
2answers
31 views

Deriving probability densitys

How does one derive probability densitys involving fractions? For example, let $X^2$ and $Y^2$ be exponentially distributed random variables with parameter $\lambda = 1$. Determine the PDF for $Z = ...
0
votes
0answers
52 views

Deterministic seeded shuffle

How can I find an injective function $f$ so that mapping that function over each element of the ordered sequence $[1\cdots{n}]$, yields a deterministic shuffle (random permutation) that is "good" ...
0
votes
1answer
41 views

What's duplication probability of the next discrete random number?

If I already have n random numbers(between 0-100), what's the duplication probability when I random next number? This is a chart represent probability(0-100%) of this question when n is between ...
1
vote
4answers
107 views

What would be the maximum number of guesses for a random number between 1 and 9?

How many guesses could someone get wrong if they were trying to guess a number between 1 and 9, with the integer always changing with each attempt? For example: If a random number generator had ...
2
votes
1answer
113 views

What is a thorough method to manually generate a random number between 1 and 100?

The other day, I got an idea. I would like to generate a random number between 1 and 100 , however by hand. And only using simple tools like a desk clock and pen and paper. What might be a way to do ...