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

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4
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3answers
533 views

What's the chance of an explicit series of integers in a limited random distribution?

Say I collect 40 perfectly random integers between 1 and 400. What's the chance that any integer is repeated consecutively six times in such a random draw? What I'm looking for is the chance of ...
7
votes
2answers
524 views

For any irrational number such as pi, would any sequence of length n appear in its decimal places?

If pi is an irrational number that goes on infinitely forever, does it mean that I can get any sequence of numbers of any length, and somewhere in the decimals of Pi, this sequence will exist. Eg. ...
1
vote
1answer
122 views

Lower bounds on the probability that one random variable is greater than a set of others

Let $X_1, \cdots, X_n$ be $n$ random variables (not necessarily independent) such that $E[X_i] > E[X_j]$ whenever $i < j$. I am interested in obtaining lower bounds on the following probability: ...
3
votes
3answers
246 views

Definition of random

Suppose that you has to guess given a set of numbers If they are random. The mathematical expectation Is there a definition of randomness that allow this prove/test? Is even possible? if so: How ...
2
votes
1answer
90 views

Meaning of randomness in space

I am a non-math person and have a question about randomness: When generating elements from a finite set using some algorithm, it is clear what it means when saying that elements should be randomly ...
1
vote
2answers
1k views

Non repeating random number generation with x(i+1) = x(i) + increment mod m

I have to generate millions of non-repeating random numbers and came across this equation: $x_{i+1} = x_i+c \space(mod \ m)$, where c and m are relative primes and $m \geq total\ to\ be\ generated$. ...
33
votes
5answers
5k views

How to find a random axis or unit vector in 3D?

I would like to generate a random axis or unit vector in 3D. In 2D it would be easy, I could just pick an angle between 0 and 2*Pi and use the unit vector pointing in that direction. But in 3D I ...
0
votes
2answers
3k views

How to Generate Random Mathematical Equations that Equal an Integer

Looking for a way to generate random mathematical equations that equal an integer between 0 and 9, a way to rank the complexity of the equation rendered, and a method to note the mathematical concepts ...
6
votes
2answers
1k views

How/why does this noise function work?

How/why does this noise function work? ...
1
vote
1answer
753 views

Doubt in Discrete-Event System Simulation by Jerry Banks,4th Edition

I'm new to the Math forum here, so pardon my question if it seems juvenile to some. I've googled intensively,gone through wikipedia,wolfram and after hitting dead ends everywhere have resorted to this ...
7
votes
2answers
936 views

How to generate REAL random numbers with some random and pseudo random

I'm doing (with Java) a very simple simulator (Queueing Systems..) that needs many random numbers (more than $10^5$). I know that Java Random class would give me all the random numbers I need, and ...
1
vote
3answers
634 views

Probability of an RNG?

For fun (relatively speaking), I'd like to do a little research on probabilities related to a pseudo-random number generator. Specifically, how would I get started figuring out "what is the ...
1
vote
0answers
325 views

Normal distribution times a log-normal distribution

First of all, am I correct in assuming that given a normally distributed random variable A, and an independent log-normally distributed random variable B, the random variable A·B is normally ...
3
votes
1answer
153 views

Uniform PRNG for long integer structures

Good morning! I don't actually know where to attribute this question (maybe it's better to publish it on StackOverflow), but it's more related to math theory than to actual realization. Since the ...
3
votes
2answers
189 views

Expected value of the product of the sum of a specific distribution

How can we find the value of the following term, $$ E[\prod_{i = 1}^{L}{\sum_{j = 1}^{K}{a_{ij}}}] $$ i.e., the expected value of the product of the sum of $a_{ij}$'s where $a_{ij}$ is a random ...
1
vote
1answer
212 views

bound of Erlang distribution

Is there any known polynomial bound of the Erlang distribution? I'd like to say that, given $k$ and $\lambda$ with probability p the r.v. is going to be less than some value x.
3
votes
1answer
166 views

Can $BPP \subset P/poly$ be strengthened to a single infinitely long advice?

It is well known that $BPP \subset P/poly$, by probabilistic method. Can this be strengthened: Is there a single string $a \in \{0,1\}^{\omega}$ such that there's a polynomial time deterministic ...
4
votes
1answer
216 views

Power Mean Random Distribution

I'm trying to find a the distribution for the power mean of $n$ random variables on $[0,1]$. I've got the arithmetic mean: $\frac{n}{(n-1)!}\sum_{k=0}^{\lfloor ...
1
vote
2answers
1k views

pdf of combination of two distinct exponential random variables

Say X and Y are two independent random variables with exponential density\begin{split} f_{X}(x) = a e^{-ax}\end{split} and \begin{split} f_{Y}(y) = b e^{-by}\end{split}, then what is the probability ...
2
votes
2answers
216 views

Are there any random variables so that E[XY] exists, but E[X] or E[Y] doesn't?

Are there any random variables so that E[XY] exists, but E[X] or E[Y] doesn't?
1
vote
2answers
286 views

Are there any random variables so that E[X] and E[Y] exist but E[XY] doesn't?

Are there any random variables so that E[X] and E[Y] exist but E[XY] doesn't?
4
votes
2answers
1k 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 ...
6
votes
1answer
389 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
votes
3answers
673 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 ...
10
votes
3answers
11k 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 ...
6
votes
2answers
383 views

number of reverses of direction to return in random walk

I am wondering if there are some studies about the number of reverses of direction to return to the starting point in random walk (either symmetric or non-symmetric), for example, its distribution and ...
2
votes
2answers
359 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
votes
2answers
97 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 ...
0
votes
1answer
113 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 ...
2
votes
0answers
129 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 ...
8
votes
2answers
9k 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 ...
3
votes
1answer
218 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 ...
13
votes
3answers
4k 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
votes
3answers
2k 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
votes
1answer
1k 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 ...
3
votes
2answers
2k 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
127 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 ...
2
votes
1answer
389 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
394 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
266 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 ...
0
votes
1answer
315 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
603 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
215 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): ...
3
votes
0answers
1k 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 ...
16
votes
4answers
535 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
votes
3answers
1k 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
2answers
387 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
319 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 ...
7
votes
2answers
580 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 ...
10
votes
2answers
198 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.