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

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1answer
23 views

The relation between the entropy of random variables $X$ and $Y=g(X)$

A previous post has shown that for random variables $X$ and $Y=bX$, where $b > 0$, the entropy of $X$ and $Y$ are not equal (Entropy of $Y=bX$). However, wouldn't any bijection $g$ on a random ...
0
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0answers
67 views

How to best randomly shuffle DNA sequence

I seek some help with how best to randomly shuffle DNA sequences. I have a long DNA sequence (lets say 100MB long = 10^8 letters) Using a 3rd party software tool, I am looking for a certain feature ...
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0answers
28 views

How many shuffles are really needed for bridge?

According to the Gilbert-Shannon-Reeds model (which apparently models reality well), one should riffle shuffle seven times to achieve a suitably randomized $52$ card deck. However, it occurs to me ...
23
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5answers
4k views

Method of generating random numbers that sum to 100 - is this truly random?

I am writing a computer program that involves generating 4 random numbers, a, b, c, and d, the sum of which should equal 100. Here is the method I first came up with to achieve that goal, in ...
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0answers
19 views

Modifying a generator of random numbers from a trapezoidal distribution to include growth and decay rates

I've written a C# random number generator based on page 11 of this paper: http://pubs.usgs.gov/tm/04/c03/tm4-C3_final_508_files/tm4-C3_apdx1_v030813.pdf It works fine but I would like to modify it, ...
-1
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1answer
58 views

Generating a random num from a triangular distribution [duplicate]

http://en.wikipedia.org/wiki/Triangular_distribution#cite_note-1 under "Generating Triangular-distributed random variates" given that U is a number between 0 and 1, what happens if the a, b and c ...
0
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1answer
29 views

(Random Sampling + Approximate Probability + Normal Approximation)

Suppose that 16% of the population of the U.S. is left-handed. If a random sample of 130 people from the U.S. is chosen, approximate the probability that at least 20 are left-handed. Use the normal ...
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0answers
24 views

How would one generate a set of $x$ random values conforming to a certain criteria?

I basically want to generate a set of $x$ numbers given $x$, a minimum, maximum and average. The set of numbers must conform, yielding the given average, with the smallest number being the given ...
0
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1answer
44 views

Generate random number based on a certain pattern and able to test against the pattern

I have very little idea about random numbers and patterns, so I am not sure whether this is actually possible or not. I want to generate random numbers, that will follow a fixed pattern (perhaps this ...
6
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1answer
91 views

What is a formal definition of 'randomness'?

What is a rigorous mathematical/logical definition of 'randomness'? Under what conditions can we truthfully apply the predicate 'is random'?
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2answers
53 views

Why is the max of x modulo m m-1?

For a sixth grade science project I asked how to scale the following formula: $X_{n+1} = (a X_n + b)\, \textrm{mod}\, m$ And in the answer (Which did work) They said that x generates whole numbers ...
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1answer
34 views

Let $X$ and $Y$ be two uniformly distributed random variables on $[0,1]$. Find $E(X^k)$ and $E(XY^k)$.

Let $X$ and $Y$ be two uniformly distributed random variables on $[0,1]$. Find $E(X^k)$ and $E(XY^k)$. How can you do this? Do you need the change of variables technique? I am a bit confused about ...
2
votes
1answer
29 views

Random number generator from a piecewise PDF

I'm trying to create a random number generator on the interval $(a,c)$ given a probability density function defined as: $$f(x) = \left\{ \begin{array}{lr} \dfrac{C}{x} &, x \in (a,b)\\ ...
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1answer
79 views

probability, random walk, Markov chain question

Let $P$ be a transition matrix for a regular Markov chain and let $w$ be it’s equilibrium vector. Show that $w$ has no zero entries.
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0answers
21 views

correlation between minimum singular values of submatrices

I have one question regarding how to measure the correlation between minimum singular values of submatrices extracted from a large random matrix. Given a m*n random matrix $\mathbf{A}$, the ...
0
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0answers
57 views

Approximation for Coupon Collector Probability

I was calculating the probability to draw all items in a list of N items, by picking one randomly, replacing it in the list, etc. (Edit: It's the Coupon collector Problem) I found this formula after ...
4
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1answer
99 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 ...
4
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1answer
96 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
22 views

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 ...
4
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3answers
93 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 ...
0
votes
1answer
44 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 ...
2
votes
1answer
130 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 ...
2
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3answers
53 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 ...
1
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2answers
83 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 ...
0
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2answers
32 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 ...
0
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1answer
21 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 ...
4
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1answer
82 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
69 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
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1answer
31 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
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1answer
31 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
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1answer
59 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
40 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
61 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
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1answer
99 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
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1answer
22 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
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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
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1answer
114 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
67 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
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1answer
67 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
10 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
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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
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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
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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
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1answer
40 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
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1answer
39 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
49 views

Covariance and correlation of summations of independent random variables

This is the problem: There are 2n βˆ’ 1 independent random variables X1, 𝑋2, ... , 𝑋2π‘›βˆ’1. The expectation E(Xi) is ΞΌ for all i = 1,...,2nβˆ’1. The variance Var(Xi) is Οƒ2 for all i = 1,...,2nβˆ’1. Let ...
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0answers
41 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
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2answers
118 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
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0answers
24 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
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 ...