Questions relating to (pseudo)randomness, random oracles, and stochastic processes.
Questions tagged [random]
1860 questions
21
votes
5 answers
So what really is a random variable?
I've been confused about the definition of a stochastic (random) variable for an embarrassingly long amount of time.
From the Wikipedia entry on Stochastic Processes, I could gather that a random variable is a map from a probability space…
user67803
17
votes
3 answers
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 positive whole number. Let's say that it has done its…
Colin
- 171
10
votes
2 answers
Pseudo Random Number Generation on the GPU
Idea
For a Path Tracing application I need to generate good quality pseudo random numbers in the closed range [0~1]. Because I'm doing this on the GPU (HLSL Shader Model 5) I can only use 32bit variables. My initial approach is the following…
Roy T.
- 437
9
votes
2 answers
How does one interpret the meaning of a stochastic derivative?
My understanding of derivatives is in the difference quotient limit sense... How does one interpret the meaning of a stochastic derivative? How can one possibly differentiate a random variable? What is its physical meaning, if it has any?
Paul
- 2,133
9
votes
3 answers
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 tried to use sines and cosines but that does not…
LCFactorization
- 2,092
9
votes
4 answers
What is a thorough method to manually generate a random number between $1$ and $100$?
The other day, I got an idea. I would like to generate a random number between $1$ and $100$ , however by hand. You often want to use these random numbers to play games or even for practical purposes.
And only using simple tools like a desk clock…
Caffeinated
- 521
8
votes
3 answers
How do we check Randomness?
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 keep asking him for the $n$-th digit and he will…
xzhu
- 4,193
7
votes
3 answers
How random is my deck of cards?
I play a few card games, and I thought it would be fun to write a card shuffling program, to see how many shuffles it takes to randomize the deck.
The algorithm is:
Cut the deck in the middle ± random offset.
while one hand is still full, place a…
AncientSwordRage
- 572
6
votes
1 answer
Is this a well-known pseudo-random number generator?
I have a pseudo-random number generator, that I am trying to understand. I have no relevant knowledge about math. I'm hoping that you can identify if this is a well-known algorithm and what its name is, so I can read a little about it.
This is the…
Daniel
- 163
6
votes
2 answers
How to quantify randomness?
I am testing a thought experiment I came up with involving the relationship between the randomness within a deck of cards and the number of shuffles. The only problem is that I do not have a way to quantify "randomness." I initially thought about…
GracefulLemming
- 261
6
votes
1 answer
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 $\rho$ respectively? Is there a known method for…
LBJ
- 157
- 1
- 7
5
votes
1 answer
Generate a pseudo random, predictable non-repeating integer sequence purely mathematically.
Let's say I have a range of integer values (could be anything but let's choose 1000000 to 9999999).
I want to begin by choosing a number somewhere within that range. I really don't care which one, it could be the first, last or random.
From that…
David Wylie
- 153
- 6
5
votes
1 answer
Shared distrustful random number generation
Alice and Bob are stingy, honorable, but also distrustful. They live far away from each other. They both know that they are the only two people who wants to buy an item in an upcoming auction. If only one of them places a qualifying bid, that person…
Jostein Trondal
- 378
5
votes
4 answers
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. IE: php rand(). What's the formula that's used…
bradenkeith
- 197
4
votes
1 answer
What is the most important test for a uniform random number generator?
What is the most important test for a uniform random number generator ? Is there a single most important test or a set? I am a using some analytically arrived at answers to probability problems and checking the simulation answers obtained through…
