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

learn more… | top users | synonyms

113
votes
23answers
10k views

Can a coin with an unknown bias be treated as fair?

This morning, I wanted to flip a coin to make a decision but no coins were in reach. There was however an SD card on my desk: Given that I don't know the bias of this SD card, would flipping it be ...
31
votes
3answers
6k views

Making 400k random choices from 400k samples seems to always end up with 63% distinct choices, why?

I have a very simple simulation program, the sequence is: Create an array of 400k elements Use a PRNG to pick an index, and mark the element (repeat 400k times) Count number of marked elements. An ...
30
votes
3answers
4k views

Why does this not seem to be random?

I was running a procedure to be like one of those games were people try to guess a number between 1 and 100 where there are 100 people guessing.I then averaged how many different guesses there are. ...
28
votes
5answers
2k 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 ...
17
votes
8answers
2k views

3 random numbers to describe point on a sphere [duplicate]

I'm currently working on a problem involving computer graphics and got into a discussion about whatever or not constructing a 3d vector out of 3 random points uniformly distributed points between -1 ...
17
votes
7answers
3k views

Generate a random direction within a cone

I have a normalized 3D vector giving a direction and an angle that forms a cone around it, something like this: I'd like to generate a random, uniformly distributed normalized vector for a ...
16
votes
4answers
434 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 ...
13
votes
4answers
6k views

Picking random points in the volume of sphere with uniform probability

I have a sphere of radius $R_{s}$, and I would like to pick random points in its volume with uniform probability. How can I do so while preventing any sort of clustering around poles or the center of ...
13
votes
4answers
555 views

How to efficiently generate five numbers that add to one?

I have access to a random number generator that generates numbers from 0 to 1. Using this, I want to find five random numbers that add up to 1. How can I do this using the smallest number of steps ...
13
votes
3answers
1k views

choose a random number between 0 and 1 and record its value. and keep doing it until the sum of the numbers exceeds 1. how many tries?

choose a random number between 0 and 1 and record its value. Do this again and add the second number to the first number. Keep doing this until the sum of the numbers exceeds 1. What's the expected ...
13
votes
2answers
206 views

$e$ popping up in topic I'm unfamiliar with

I programmed up a little algorithm that goes like this: Fix two positive, real numbers, call them $\alpha$ and $\beta$. Generate a new, random, real number, $x \in [0,1]$ Set $\alpha$ = ...
12
votes
2answers
984 views

Apparent Paradox in the Idea of Random Numbers

This question is a bit less than rigorous, but it's only because I don't know how to formulate it rigorously. Suppose there was some machine, or function, or whatever that could output a random ...
12
votes
1answer
255 views

Does $\pi$ satisfy the law of the iterated logarithm?

It is widely conjectured that $\pi$ is normal in base $2$. But what about the law of the iterated logarithm? Namely, if $x_n$ is the $n$th binary digit of $\pi$, does it seem likely (from ...
11
votes
2answers
584 views

Are primes randomly distributed?

There is a famous citation that says "It is evident that the primes are randomly distributed but, unfortunately, we don't know what 'random' means." R. C. Vaughan (February 1990) I have this very ...
10
votes
6answers
2k views

Choosing two random numbers in $(0,1)$ what is the probability that sum of them is more than $1$?

Choosing two random numbers in $(0,1)$ what is the probability that sum of them is more than $1$? Also what is probability of sum of them being less than $1$? I think the answer should be ...
10
votes
7answers
596 views

Can true randomness come out of mathematical rules?

For example, prime numbers, they seem very random, and they are defined by a simple set of rules. I can't see how real randomness could exist in the real world, but what about mathematics?
10
votes
3answers
2k views

Is there a “most random” state in Rubik's cube?

Is there a state in Rubik's cube which can be considered to have the highest degree of randomness (maximum entropy?) asssuming that the solved Rubik's cube has the lowest?
10
votes
5answers
372 views

Why do we need “perfectly” random numbers?

I periodically see articles about physicists or others coming up with a technique that generates a slightly more random number than was possible before, and how this is useful for encryption. But ...
10
votes
3answers
361 views

Generation of unimodular matrices with bounded elements

Does anybody know what is the algorithm for generating random unimodular matrices (integer matrices with determinant $\pm 1$) whose elements do not exceed a given bound? Such an algorithm is mentioned ...
9
votes
2answers
2k views

How can I pick a random point on the surface of a sphere with equal distribution?

I've got a random number generator that yields values between 0 and 1, and I'd like to use it to select a random point on the surface of a sphere where all points on the sphere are equally likely. ...
9
votes
2answers
179 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.
8
votes
3answers
1k 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 ...
8
votes
3answers
458 views

How do we check Randomness? [duplicate]

Let's imagine a guy who claims to possess a machine that can each time produce a completely random series of 0/1 digits (e.g. $1,0,0,1,1,0,1,1,1,...$). And each time after he generates one, you can ...
8
votes
2answers
819 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 ...
8
votes
1answer
276 views

Repeatedly Toss Balls into Bins

$n$ balls are randomly tossed into $m$ bins, each bin can hold $k$ balls. If a ball is tossed into a full bin (already has $k$ balls in it), it can be tossed repeatedly and randomly into the $m$ bins ...
7
votes
4answers
5k views

What's the difference between stochastic and random?

What's the difference between stochastic and random? I've read in the portuguese wikipedia that there's a difference, but I still didn't see this point on english wikipedia.
7
votes
2answers
291 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 ...
7
votes
2answers
460 views

Probability that a sequence repeats itself

Given an infinite sequence $a_n$ of uniformly random integers $0$ to $9$, what is the probability there exist an integer $m$ such that the sequence $a_1$ to $a_m$ is equal to that from $a_{m+1}$ to ...
6
votes
4answers
1k views

Are irrational numbers completely random?

As far as I know the decimal numbers in any irrational appear randomly showing no pattern. Hence it may not be possible to predict the $n^{th}$ decimal point without any calculations. So I was ...
6
votes
2answers
599 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 ...
6
votes
2answers
386 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. ...
6
votes
3answers
8k 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
328 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 ...
6
votes
1answer
1k views

The parking problem riddle

Assume a street of 300 meters, that you can park your car alongside the pavement. Assume that there is a big parking problem in the area. Assume that the pavement is continuous, without interruptions, ...
6
votes
1answer
189 views

If W is a random matrix with variance $\mathbb{E}[W W^{T}]$, what's $\mathbb{E}[W^{T} P W]$?

I know quite a few identities about quadratic forms of random vectors, but I'm having difficulty coaxing something out of this quadratic form of random matrices. Suppose I know $\mathbb{E}[W W^{T}]$ ...
5
votes
2answers
292 views

Name this paradox about most common first digits in numbers

I remember hearing about a paradox (not a real paradox, more of a surprising oddity) about frequency of the first digit in a random number being most likely 1, second most likely 2, etc. This was for ...
5
votes
2answers
1k views

What is golden ratio doing in this computer code?

In this file (related to random number generation), there is following line: private const int MSEED = 161803398; which reminds on golden ratio. How come ...
5
votes
2answers
490 views

Summing (0,1) uniform random variables up to 1 [duplicate]

Possible Duplicate: choose a random number between 0 and 1 and record its value. and keep doing it until the sum of the numbers exceeds 1. how many tries? So I'm reading a book about ...
5
votes
2answers
196 views

Finding the probability that a student is a random guesser

I want to find the probability that my student is a random guesser. On a 360-item multiple choice test with four choices for each question, he got 28.5% or 103 of the questions correctly. Here is ...
5
votes
1answer
589 views

How can we generate pairs of correlated random numbers?

If I can generate normal random numbers in $N(0,1)$, how can I generate two dependent random numbers, $Y_1$ and $Y_2$ with means $\mu_1$, $\mu_2$ and $\sigma_1$, $\sigma_2$ and correlation coefficient ...
5
votes
2answers
732 views

Random number generation inside an interval based on cdf (Zipf and Exponential)

Consider for example the Exponential distribution with c.d.f. $F(x) = 1-e^{-\lambda x}$. $F^{-1}(x)$ would be inverse cdf (quantile function). If I generate y=F−1(x) with x uniformily distributed on ...
5
votes
3answers
172 views

Does an n-order Markov chain still represent a Markov process?

I am trying to understand Markov processes but am still confused by their definition. In particular, the Wikipedia page gives this example of a non-Markov process. The example is of pulling different ...
5
votes
1answer
144 views

A consequence of the law of large numbers

Let $(X_k)_{k=1}$ be Poisson random variables with expectation $\mu$, let $Y_n = \sum_{k=1}^{n} X_k$. The weak law of large numbers states that, $$ \forall \delta>0, \forall \epsilon>0 \, \, ...
5
votes
1answer
513 views

Generating geometrically-distributed variates over an interval given endpoints and expected value

I want to generate random variates from a truncated geometric distribution over the interval $[0, n)$ with specified expected value, $0 \le E < n$. The obvious way to do this seems to be to sample ...
5
votes
1answer
54 views

Why does adding 3 random decimals in the range [-1,1] give a normal dist with std. dev 1?

I've used Math.random()*2-1+Math.random()*2-1+Math.random()*2-1 many times in the past to get normally-distributed random numbers with a standard deviation of 1. ...
5
votes
1answer
303 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 ...
5
votes
1answer
186 views

Asymptotics of sum of binomial distributions

Definition 1: For any random variable $X$, we define $\mathrm{Bin}(p,X)$ as a variable with binomial distribution having parameters $p$ and $X$. Definition 2: For all $i \in \mathbb{N}$, define ...
5
votes
1answer
70 views

Interpretation of a simple probabilistic term in a calculation

I'm reading through my notes on the evolution of random graphs and have come unstuck trying to figure out the meaning of a probabilistic term which appears, and was hoping you could help - it's not ...
5
votes
1answer
883 views

How/why does this noise function work?

How/why does this noise function work? ...
5
votes
1answer
308 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 ...