# Tagged Questions

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

12k 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 ...
1k views

### Mathematicians shocked(?) to find pattern in prime numbers

There is an interesting recent article "Mathematicians shocked to find pattern in "random" prime numbers" in New Scientist. (Don't you love math titles in the popular press? Compare to the source ...
5k 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. <...
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 ...
6k 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 don'...
15k 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.
14k 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 ...
7k 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 ...
3k 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 ...
7k 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 ...
3k 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 ...
3k views

### Choose a random number between 0 and 1 and record its value. Keep doing it until the sum of the numbers exceeds 1. How many tries do we have to do?

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 ...
569 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 ...
411 views

### Flaw or not flaw in Excel's RNG?

I have a question about my understanding of an article of B.D. McCullough (2008) about Excel's implementation of the Wichmann-Hill random number generator (1982). First, a bit of context The ...
5k 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?
5k views

### Markov process vs. markov chain vs. random process vs. stochastic process vs. collection of random variables

I'm trying to understand each of the above terms, and I'm having a lot of trouble deciphering the difference between them (note, my mathematics training isn't very strong - so please go easy on the ...
486 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 ...
5k 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 ...
4k views

177 views

### Fitting a parabola to separate two classes of points in the plane

Suppose we have a set of points $(x,y)$ in the plane where each point is either boy or a girl. Does there exists a randomized linear-time algorithm to determine if we can fit a parabola (given by a ...
12k 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 ...
776 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 ...
649 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?
2k 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 ...
795 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 I'...
199 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.
896 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 ...
10k views

455 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'?
176 views

### How to attack universal hash function based on finite-field arithmetic?

As per the Recursive n-gram hashing is pairwise independent, at best paper, I want to use the algorithm described in chapter 6 and 7 (page 7 - 10). The hash works as follows: Define a random ...
Say there exists a limit $\lim_{x \to x_0}f(x) = L$. Is it necessary that $f$ be defined at the point $x_0$ itself? Well, what I think of it is that it's OK to be undefined at that point because I ...