Questions tagged [random]

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

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6 views

Calculate the seed of a PRNG from a list of random numbers

Lets say i have a list of randomly generated numbers. Example: import random i=1 mn = 1 mx = 2 while i<500: print(random.randint(mn,mx)) i=i+1 Only ...
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24 views

Concentration of the number of edges inside a random induced subgraph

Let $G=(V, E)$ be an arbitrary graph with $n := |V|$ vertices and let $r \leq n$ be a parameter. Let $U \subseteq V$ be a subset of size $r$, chosen uniformly at random from the set of all subsets of $...
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18 views

Searching with a 1D car?

Consider the task of programming a 1D car starting on point $0$. The car drives 1 km / min ( to both left and right). The task is to find a coin at an unknown integer distance $x$ (in km) from the ...
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18 views

Are there any plausible definitions for a random oracle in the real numbers? [closed]

I.e., is there any plausible definition for choosing a random point from the real numbers.
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Sum of Joint and Conditional Probability Mass Functions [closed]

let's consider a pair (X,Y) of discrete random variables, and suppose X can assume values x in A and Y can assume values y in B. Now,
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8 views

Finding value of a simple Pseudo random number generation function

I have an equation to generate pseudo-random numbers, example function is well-known called Linear congruential generator(LCG). The function definition is like ...
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1answer
14 views

Place (Scatter) random rectangles in a bigger rectangle

I am making a voxel game and creating the terrain, The ground and elements on it are rectangles, First of all I want to generate the elements guaranteed that their total area is less than ground ...
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1answer
22 views

Solovay's lemma for a non-computable sum

I'm currently learning about computability theory, specifically about Martin-Löf randomness. In this paper by M. Pancia, I came across an interesting result called Solovay's lemma (below, I give the ...
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1answer
29 views

Expected value of a recursive random function

function foo(n) if n = 1 then return randint(INT_MAX) else return randint(foo(n-1)) end if end function The idea is ...
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11 views

Non-uniform random point scatter

I'm looking for an algorithm to scatter points in a confined 2D space at random. I'd like the randomness should have these properties: There's a function f(x,y), say between [0,1] that defines a ...
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2answers
57 views

Formal statement of property of randomness of a sequence

Suppose we have a probability space $(\Omega,{\mathscr F},P)$ consisting of An arbitrary nonempty set $\Omega$ A collection ${\mathscr F}$ of subsets of $\Omega$ which is also a $\sigma$-algebra on ...
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25 views

Solve the problem with numbers from 1 to 101 written in a random order

Numbers from 1 to 101 are written in a row in a random order forming a list. Prove that you can remove 90 numbers from this list such that remaining numbers will be sorted in the ascending or ...
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14 views

How to measure permutation randomness in the following situation?

I am thinking of optimizing a computer system and I want to implement permutations of $9$ using permutations of $3$ [case 2] Case1: Lets say I have permutation $9$ numbers $0,1,2,...,8$. $9! = 362880$...
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30 views

Is there a way of generating true random numbers only using pure maths?

I know that true random numbers can be generated using measurements taken from the atmosphere, but is there any way of doing this mathematically, without any measurements taken from the external world?...
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Simulate a model including random variable and known dataset

I took simulation as a tool of uncertainty propagation. My model-for-solving looks like this: $Y= X_1 \cdot X_2\cdot X_3\cdot X_4$ I found good data on $X_1(n=1000)$. For $X_2, X_3 and X_4$ I also ...
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33 views

Random pairing of elements between two sets

I need an efficient ($O(n)$) algorithm that pairs two sets of objects. So given $A=\{a_1, a_2, ..., a_n\}$ and $B=\{b_1, b_2, ... b_m\}$, I need to find $N=\textrm{min}(n, m)$ number of random (...
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33 views

Why do Random Walks always get back in 2D but not 3d?

I'm aware that Random Walks always end up where it started in 2D but not in 3D. All the videos online are simulation-based, but does anyone know what the mathematical proof is?
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25 views

The probability of a random interval

Let's consider a unit interval $[0,1]$ and a subinterval $I \subset [0,1]$. The subinterval $I$ has the following features (1) Every element $i \in I$ is randomly and uniformly picked from $[0,1]$ ...
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34 views

What is the probability distribution of a random variable with distribution function $F_{Y-X}(z)=1-\frac{\nu}{\nu+\lambda} e^{-\lambda z}$?

I have this: $F_{Y-X}(z)=1-\frac{\nu}{\nu+\lambda} e^{-\lambda z}$. I have to find a probability distribution to work with and then obtain $E(Y-X)$ and some other data based on the distribution ...
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28 views

Will linear interpolation of a random value from one range to another 'preserve' randomness?

I have generated a number z from a range (x,y) and want to map z to another range (p,q) This can be achieved using linear interpolation as seen here: https://www.mathworks.com/matlabcentral/answers/...
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1answer
33 views

$\inf$ and $\sup$ of two real random variables

Let $X$ and $Y$ be two rrv’s. Prove that $\inf(X,Y)(w):=\inf \{X(w),Y(w)\}$,$w\in \Omega$ and $\sup(X,Y)(w):=\sup\{X(w),Y(w)\}$, $w\in \Omega$ are also rrv’s. In the book, definition of real random ...
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1answer
24 views

Randomness of deterministic dynamical system

I was told by someone that there are results which show that an observation of certain deterministic dynamical systems can not be statistically distinguished from stochastic noise. Can someone point ...
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31 views

Combinatorics Issue with Long Expression

So I have this strange issue that I'm not sure how to resolve. If x, y, and z are randomly chosen integers from a set {1, 2, 3... 2016} and I need the probability that $6z - 3yz + xyz - 4xy + 8x + 12y ...
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1answer
24 views

Period of a Linear congruential generator

I found by experimentation that for the pseudorandom generator described below, the period is 32 (https://repl.it/repls/EasySphericalPhysics). $X_0=0$ $X_{n+1}=(34 * X_n + 17) \bmod 97$ Although ...
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14 views

mean square continuous and diferentiable

Random Process $\{X(t) = min(t,\tau), t \geq 0\}$, where $\tau$ is an $Exp(\lambda)$-distibutet random variable. Prove that X is mean square continuous and mean square differentiable. So for mean ...
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25 views

How to get probability of getting only those items from box which you did not pick before?

I have a box which contains $n$ unused items (all items in the box are unused). From them I randomly pick $k$, where $k < n$ items. Those $k$ items became used when I picked them, and then I put ...
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38 views

How does the Random Number Generator work?

I've always wondered that if computers or calculators for that matter work exactly the way we program them, then how is it possible for them to generate random numbers that are unbiased. How do they ...
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11 views

the magnitude of what complex random distribution yields a weibull distribution?

I need a complex random number generator whose magnitude is a Weibull distributed random number. In other words: take 2 independent identically distributed random numbers, x & y. Calculate $z=\...
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34 views

Adding more elements to a sequence so that it have the desired probability distribution

If I need to generate N numbers from a given probability distribution, I am aware of how to do this. But my problem is out of the N numbers, say, k numbers are already fixed. (k is very small than n)....
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1answer
70 views

Estimation of autocovariance function for stationary times series

Let $\{X\}_{t\in T}$ is the times series. For observation $x_1,x_2, x_3,\dots x_n$ of a time series the sample mean is $$\hat\mu=\frac{1}{n}\sum_{t=1}^{n}x_i$$ and the sample autocovariance function ...
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34 views

algorithm for triangular surface elements enclosing random 3D points

Suppose 3d space has certain number of random points. All these points can be enclosed on a surface made up of triangular elements such that vertices of these triangles are the random points with the ...
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32 views

Probability of a real random uniform distributed number is picked $>t$ times before all other possible numbers have been picked at least once?

Given a real random number generator with uniform distribution of values between $1$ and $N$. The random number series ends if all values between $1$ and $N$ have been picked at least once. How high ...
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13 views

Is there a (pseudo) random value function with $r_{n+1} = f(r_n)$ which produces a permutation from $1$ to $N$ without a close form for $r_n$

There should not exists a close form for $r_n$. It should look like: $$ r_n = f(r_{n-1})$$ So to compute the next value the prior value is needed. (Function $f$ need to be computable at PC also for ...
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Why is Knuth's definition of random sequence (R4) too weak?

Knuth's $R4$ definition of a random sequence is called "too weak" and he presents an example of why --- second paragraph after the definition on the previous link. Definition $R4$. A $[0..1)$ ...
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25 views

Is there a (pseudo random) value generator $r$ with $\sum_{i=1}^N r_i \equiv 0 \mod N$ and $|\{\sum_{i=1}^j r_i \mod N, \forall j<=N\}|=N$

Or as weaker version also works with $M<=N$ (but $M>=\sqrt[3]{N}$, $N$ >1000): $$\sum_{i=1}^M r_i \equiv 0 \mod N$$ and $$ S = \{s_j = \sum_{i=1}^j r_i \mod N, \forall j<=M\}$$ $$|S|=M$$ ...
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67 views

Are there some commutative function to produce (pseudo) random numbers?

I'm looking for functions $f_1, f_2$ which are commutative to each other. $$f_1(f_2(x)) = f_2(f_1(x))$$ Random numbers $r_{i,j}$ should be computed in a chain/sequence: $$r_{i+1,j} = f_1(r(i,j)) $$ $...
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24 views

How can the Johnson-Lindenstrauss Lemma be true, intuitively?

I have read this article about Johnson-Lindenstrauss Lemma can preserve distance-related property from reduced high-dimension matrix only by multiply it with random matrix with standard normal ...
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looking for functions that are randomized, aperiodic, non-recursive, … (help my terminology)

Context I'm creating a video game with a generated world that can be very large in scale (beyond what will fit on the machine). I want to have some very large objects, where the user might only be ...
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1answer
67 views

What does “Random Rotation Matrix” really mean? How to generate it?

I got the term from this paper[1] and I don't understand what it means. It said the "Random Rotation Matrix" can be generated following "Haar Distribution"[2]. I only know the output is a matrix which ...
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22 views

Why generating Pseudo-random Numbers by Linear Congruential Generator, the X will follow a uniform distribution?

To be specific, attached is the algorithm of LCG: My question is why X follows a uniform distribution while generating X in this way? And why we use this way to generate X which follows uniform ...
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7 views

Is it possible to change the order of random samples such that no statistical test can detect the change?

Consider I have a 1 million fair die tosses which is will be used in a true random number generator. Can an adversary change the order (just swap a pair of numbers or two) in the sequence such that ...
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13 views

Naming continuous-time random walks

Is there a standard notation for naming continuous-time random walks according to their probability distributions? For example, Lévy flights as Cauchy-based random walk, Rayleigh walk as Gaussian-...
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1answer
36 views

How to mathematically represent pore distribution?

I'm currently working on mechanical modeling of microstructural samples and I have a question. Can anyone tell me is there a way to mathematically express distribution of pores in a certain area. I ...
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23 views

random natural number from range using negative binomial

How can you extract a random number from a range using the negative binomial distribution? For example: the range of possible result values is [1,10] the probability of success is 0.2 I really don'...
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59 views

Impossibility of deriving the Born Rule?

Background Let's say I have a physical system. When a measurement happens we apply the Born rule to say which outcome is likely. Now, while a lot of physicists are of the opinion the measurement is ...
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1answer
57 views

Random walk on $x$-axis - Probabilities

Exercise : A particle is moving randomly on the $x$-axis. At each instance of time, it moves either right with probability of $p$ or left with probability $1-p$. Each step of movement is ...
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1answer
87 views

expected hitting time of asymmetric random walk

$X_1$, $X_2$, ... are i.i.d. random variables with distribution P($X_i$ = 1) = $\frac{2}{3}$, P($X_i$ = -1) = $\frac{1}{3}$. Let $$S_n = \sum_{i=1}^n X_i$$ For each integer k > 0, define $$T_k = min \...
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22 views

question about Random probability measures

Let $(\Omega,\mathcal{F},P)$ be a probability space and $X$ be a Polish space. Let $\mu:\Omega\rightarrow Pr(X)$ be a random probability measure with marginal $P$ on $\Omega$ and $\mu_\omega$ be the ...
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3answers
93 views

Pen and paper pseudo-random number generator

tl;dr How can I generate pseudo-random numbers using only pen and paper? Uniform distribution (or as close as possible) It's pen writing on paper; can't cut, fold, throw or anything like that I'm ...
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Finding a function to produce specific expectation.

$X$ is a random variable with known pdf. I do have the expectation of a function of X. $\mathbb{E}[f(X)] = A $. Is f unique? I also have multiple sets of vector $(x_1, ..., x_n)_t$ known, where $t$ ...