Questions relating to (pseudo)randomness, random oracles, and stochastic processes.
Questions tagged [random]
1860 questions
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Unfair coin vs Random algorithm
I had bought an unfair coin. The probability of getting a tail is 75% P(T) = 3/4 and the probability of getting a head is 25% P(H) = 1/4
I decided to do the following experiment: I programmed a computer to generate a random boolean.
TRUE means Head…
TSR
- 507
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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 LFSR, of course, if k < the degree of the characteristic polynomial)
edit: I am also…
Jason S
- 3,109
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What is the average size of all continuous unicolored areas in a randomly colored grid?
It is somewhat similar to the percolation theory, but I can't find any reference for what happens with multiple colors involved.
Let there be an infinite grid and $n$ colors. Each tile in the grid is assigned a random color (each color with…
BoltKey
- 421
3
votes
2 answers
Calculating license plate combinations
If there are $26$ available capital letters and $6$ available numbers $0$ to $9$ to complete a $6$ "digit" combination (a license plate for example) what is the formula for calculating the number of possible combinations? I am not a math major nor…
hollywood913
- 31
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Generating random vectors in a n-ring
I've seen many different approaches to generate a random vector in the ($n-1$)-sphere and in the $n$-ball. One of them is generating a normal n-vector v (all components $x_i\sim N(0,1)$) and then normalizing the vector. For some weird reason I…
Alejandro Piad
- 217
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Are these numbers "random"?
The figure below shows $2000$ points in $(x,y)$ coordinates that are supposed to be high quality pseudorandom numbers.
However, when I zoom in on any area lots of points are lined up along line segments, and there are relatively large areas with…
Ted Ersek
- 1,207
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Are there different degrees of "random" or is it exclusively a binary result?
I'd like to understand if the randomness of a sequence is boolean or if there are different degrees of randomness.
Perhaps the randomness (confidence) test of a series can be based upon
the algorithm used to determine randomness (theoretic…
makerofthings7
- 567
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Random Numbers and probability
How long does a sequence of random decimal digits (0, 1, 2, ..., 9) need to be before you can "reasonably" expect the sequence to contain all numbers from 0 through 999 (inclusive).
--
It's up to you to define "reasonably".
E.g.:
The sequence 1823…
justme
- 31
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How to efficiently sample a point in a polyhedron
I have a polyhedron $P$ described by
$$
P = \{ x | Ax \preceq b\},
$$
$x \in \mathbf{R}^{n}.$ I want to randomly generate points that are inside $P$.
One way is to just generate random points and select those that satisfy the inequality but…
Petch Puttichai
- 637
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1 answer
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 can be stated as
Find the period of a "black…
J. M. ain't a mathematician
- 75,051
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What is the test of for randomness
How do you tell if a large sequential sample taken from a 0-1 rectangular parent - and presented as random - is truly random?
2
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3 answers
Get random $x, y, z$ point inside a sphere?
What is the easiest way to get a random Point3D inside the sphere where is red?
lacas82
- 23
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votes
3 answers
Can a random number generator with a given number of bits have an arbitrarily long period?
Is there any upper limit for the period of any pseudo-random number generating algorithm with a fixed number of bits? I know there are some algorithms with a very large period, such as MT19937, but I wonder if it is possible to derive a theoretical…
Felix Dombek
- 345
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votes
1 answer
Transforming numbers into fake randoms that are actually deterministic
How can I convert a number into a seemingly random number in a process that is actually deterministic?
For example I'd like to transform: 123456 into 51.
Or 28. Doesn't matter as long as it's a number between 1 - 1000.
The value should be…
nicholaswmin
- 199
2
votes
1 answer
Average number of $U[0,1]$ random numbers to reach $x$
Let $P(x)$ be a random process where you keep selecting random numbers, uniformly distributed between 0 and 1, until the sum reaches $x$.
From memory, the expected value of the number of terms needed by $P(x)$ is $e^x Q(x)$, where $Q(x)$ is a…
Empy2
- 50,853