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

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2
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2answers
232 views

Why do people say that prime numbers are “random”? [closed]

Compared to most of the people who frequent this place I suppose I am not very smart, but I do have a solid basic and somewhat intuitive understanding of mathematics. Now prime numbers have always ...
1
vote
1answer
43 views

Algorithm to generate normal matrices at random

I would like to generate normal matrices by an, say python, algorithm, that produces normal matrices distributed evenly in the limit of large n. I would not like to be restricted to Hermitian matrices ...
0
votes
2answers
53 views

Distribute a population size based on fractions using random number generator drand48()

I have a population size of say 5000 people. Every person belongs to either A, B, C or D category. I want to split the population as per a given fraction provided by user. for example, 99% of A, 0.4% ...
0
votes
1answer
21 views

Looking for a random statistical biaised function

A common random function is designed like a dice, if you call it many times it will yield approximately the same number of times 1, 2, 3, 4, 5 and 6. Statistically, you could say it's equally spread ...
0
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0answers
75 views

Derive c.d.f and p.d.f of a random variable which is defined as function of two random variable

Let $x_1$ and $x_2$ are independent random variable with p.d.f $f(x_1)$ and $f(x_2)$. How to derive c.d.f and p.d.f of random variable $y$, which $y = \frac{x_1 x_2}{ax_1 x_2 + bx_1 + cx_2 + d}$ ...
0
votes
1answer
67 views

2 dimensional random walk - hit of targets

Consider a random walk in $\mathbb{Z}^2$, $x(j) = x(j-1) + \xi_j$, where the increments are random variables independent and identically distributed with finite support, the expectation $m := ...
0
votes
2answers
50 views

Finding derivative of this integral function.

I need help on finding the derivative of this: $$g(x) = \int_1^{x^2} (x-t)\sin^2(t)dt$$ I thought about taking out x and having it as a constant but how?
0
votes
0answers
29 views

Spatial randomness of 2-tuples

Lets consider a sequence of 2-tuples $\{(x_i, y_i)\}_{i=1}^n$ in a bounded 2D space. My goal is to investigate the random distribution of these 2-tuples. Can I deduce the spatial randomness of ...
1
vote
1answer
3k views

'normally distributed random numbers' vs 'uniformly distributed random number'?

what is the difference between 'normally distributed random numbers' and 'uniformly distributed random number'? A answer in a layman language is appreciated :)
4
votes
0answers
57 views

Entries of a Haar distributed unitary matrix

The eigenvector matrix of a Wishart matrix is Haar distributed and that implies that the eigenvectors are uniformly distributed on a sphere. I'm interested to know what is the distribution of ...
0
votes
1answer
97 views

how to generate Normally distributed random number?

I am looking for a function that can generate Normally distributed random numbers. I came to know about bux-muller transform but I didn't understood it completely what it is doing. Thus it would be ...
1
vote
0answers
22 views

generating locally random permutations

I have an intuitive notion of 'local randomness' that I am trying to make precise and understandable, and I am running into a bunch of problems. A quick web search failed to find anything relevant in ...
0
votes
1answer
74 views

Needed a math function, Don't know what to call it?

I need a math function $f(\ell)\to n$ whose input is a list of numbers and whose output is a noisy value (random value added to original input to get noisy output). The function $f(\cdot)$ should have ...
0
votes
1answer
77 views

random walk with dependent increment

Consider the following sort of random walk. The position of the walker at time $t$ is represented by the random variable $r(t)$, with $r(0) = 0$. The variable satisfies the following equation, $$ ...
0
votes
2answers
46 views

Pseudo random ordering of integers

I remember an old retro effect for a screen resolution of $320\times 240$. You would iterate the pixels in a linear fashion so there are $76800$ pixels. You could iterate then one by one starting at ...
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. ...
2
votes
0answers
101 views

Using an elliptic curve to create pseudo random number

I recently started learning about encryption. I read about how elliptic curves can be used to create pseudo random numbers (and how the nsa might have abused this fact to create a backdoor in ...
4
votes
3answers
172 views

Recursion with Random number?

function foo(n) if n = 1 then return 1 else return foo(rand(1, n)) end if end function If ...
0
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0answers
34 views

Explicit computable discrete pseudo random walk

Is there any algorithm that would be able to explicitely calculate a value $n_i$ for any index $i$, so that the sequence $n_0,n_1,...$ could also be a realisation of some random walk?
0
votes
1answer
89 views

What is the expected error of a randomly generated number?

Forgive me if this question is unclear, as I'm not a mathematician. The question has come up in an industrial sensor application. I am trying to make the displayed sensor value to be more steady ...
4
votes
3answers
221 views

Probability that a chosen number will be a Fibonacci number

Suppose that I randomly choose an integer $x$ with $1 \leq x \leq n$ where $n$ is a natural number. What is the probability that $x$ will be a Fibonacci number?
0
votes
1answer
45 views

Random Walks proof SOS

Given this equation: $f_{2k}2^{2k}u_{2n-2k}2^{2n-2k}$=$f_{2k}u_{2n-2k}2^{2n}$ then it asks to "sum over k" to obtain this equation: $u_{2n}2^{2n}$=$f_0u_{2n}2^{2n}+f_2u_{2n-2} ...
0
votes
0answers
23 views

Reciprocal antiderivative of a process in an expected value

Given a stochastic process $X=\left \{ X_{t}:t\in [0,T] \right \}$, with known probability and spectral density function, is there a way to calculate or estimate the following expectation: $$\left ...
1
vote
0answers
51 views

Probability of random functions where domain equals co-domain

Given random function defined by $f: [n] \rightarrow [n]$, chosen uniformly, what is probability that the function is injective, surjective, or bijective? If $[n]$ is a set of discrete elements, ...
2
votes
1answer
95 views

Probability of picked cards to be smaller than the largest picked card

I have an assignment for my algorithms module that requires us, amongst other things, to find the equations for the following question. Edit - Question Updated You have n cards with pairwise ...
0
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1answer
64 views

Probability randomly picked card is smaller than another picked card

Given a set of m cards that have values pairwise different with range 1 to m, what is the probability that after shuffling the card, and picking two of them, the first one is larger than the second ...
0
votes
0answers
51 views

Computing an estimator for a piecewise distribution?

Suppose I have a random variable $X$ that follows a distribution with a piecewise function $f(x|\theta)$. What is the correct way to compute an estimator $\theta$ for this function? Should the ...
3
votes
1answer
40 views

Find probability of a Poission process.

Given that $N=\{N(t)\mid t\geq 0\}$ is a Poisson process with parameter $\lambda>0$ I need to find $P(N(3)=2\mid N(1)=0, N(5)=4)$ So this is a conditional probability (can anyone clarify if this ...
1
vote
0answers
96 views

Randomized packing of items

An adversary gives you a set of items whose total size is $x$ (he gets to choose how $x$ is distributed. e.g. there may be $k-1$ items of size $\frac{x}{k}$ and 2 items of size $\frac{x}{2k}$). The ...
0
votes
1answer
102 views

Frequency analysis/discrete uniform distribution in multiple choice tests

I may be using the wrong terms in the title but I read that if something is random then each character will occur an equal amounts of times. I read this when reading about the One-Time Pad cipher, ...
1
vote
0answers
25 views

Determinate State of Linear Congruential Generator from Results

I am curious on how someone would go about determining the state of a Linear Congruential Generator given its output. X(n-1) = (aX(n) + c) mod p Since the values ...
5
votes
0answers
199 views

expectation value for minimum distance between random variables

note: edited to clarify boundary issue Suppose $x_i$, $i=1\dots n$, are randomly drawn from a uniform circular distribution between 0 and 1 (using periodic boundaries). Let $d_i$ be the distance ...
0
votes
0answers
29 views

Problem with an inequality from probability theory (Random matrix theory)

I read the following notes on random matrix theory http://www.umpa.ens-lyon.fr/~aguionne/cours.pdf . While reading Wigner's proof for the semi-cicular law I encoutered the following inequality on page ...
0
votes
2answers
121 views

Addition of probabilities and gambler's fallacy

Say you have a 1 in 6 chance of winning a card game. The more times you play, the higher the odds of you winning. $$P(\text{win over 1 trial}) = 1/6 \\ P(\text{win over 2 trials}) = 1/6 + 1/6 \\ ... ...
2
votes
1answer
66 views

Probability that number begins with one

I have three very similar algorithms generating very different results. In all of them I'm calculating distribution of first number of random number. First algorithm Here I'm generating random ...
0
votes
1answer
34 views

Generation of “random” multilinear polynomials for testing non-negativity algorithm

Multilinear polynomial is a multivariate polynomial where the exponent is zero or one. My instructor suggests to test my non-negativity algorithm with ...
1
vote
1answer
87 views

Plotting psuedorandom jagged parallel lines

I'm very interested in the morphogenic freehand drawings of John Franzen. I am looking to develop an algorithm which can draw lines such as these with some "entropy". That is, somewhat jagged or ...
1
vote
2answers
54 views

How to proof the randomness of a number sequence?

I've got a sequence of numbers generator by a "random number generator". Is there a way or a method to proof the randomness of the generator? How would I even compare randomness of generators? Or ...
0
votes
2answers
49 views

What is the statistical difference (if any) between these two methods of generating an n-digit random number?

To preface, this question is coming from a software developer so it's written from that perspective. If I need to generate a random number with $n$ digits, I could do it in one of two ways. a. Ask a ...
1
vote
0answers
19 views

Good notation for many random points approximating an area.

I'm trying to say that as the number of random coordinate points points you plot approaches infinity, it is equivalent to an area integral where each point is an infinitesimally small $\mathrm{d}x ...
0
votes
2answers
59 views

Exercise from probability

In normal deck of cards each of the cards have some rank (2 have rank 2, 3 have rank 3, ... , J have rank 11, Q have rank 12, K have rank 13 and A have rank 14). 3 cards are drawn. We have the random ...
1
vote
1answer
66 views

Generating Auto-Correlated Random Numbers with finite correlation length

How can I generate a lot of (for example N=20000 or more) auto-correlated random numbers {x_n, n=1,2,...,N} with uniform or normal probability distribution and finite correlation length (Here eq. ...
1
vote
1answer
54 views

How many iterations does it take to cover a range with random values?

Let's say I have a random number generator that generates integers uniformly from 0 to n-1 (where n is some positive integer). What is the expected number of iterations after which all the values ...
1
vote
0answers
37 views

explicit random cake cutting

I like to split a given interval, let's say $[0,1]$, randomly to a given number $n$ parts. A random input may be provided, like for example a sequence of random numbers $\omega=(r1, r2, ...
0
votes
1answer
40 views

Multiple independent random number streams

This question is somehow related to this one. Having multiple streams of pseudo-random numbers known to be independent and with a uniform distribution I want to do Monte Carlo simulations in ...
2
votes
0answers
74 views

How to construct a uniform joint distribution

I have a question that is critical to my work, but I am not sure if it is any possible. Assume that you have two uniform random variables X and Y. The product distribution of Z=XY is not a uniform. ...
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0answers
37 views

choose a list of words such that have equal letter frequency

I have a big list meaning full Words. surely letter frequency of this word list is different for each letter. Now my problem is to find a way to randomly select words from this word list to a new ...
1
vote
1answer
100 views

Generating a uniformly distributed set of numbers with negatives?

I have a number generator that can generate numbers between 0 and 1. I want to somehow use this generate a set of $N$ numbers that add up to $1$, and include negative numbers. These numbers must be ...
2
votes
1answer
52 views

Independent sequences

Let $\{x_i\}_{i = 1, ...,n}$ , $\{y_i\}_{i = 1, ...,n}$ be sequences generated by a pseudo-random number generator using different seed keys, for example $ x_0$ and $y_0$. Are $\{x_i\}$ and $\{y_i\}$ ...
1
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0answers
30 views

Reservoir sampling - understanding probabilites

I am reading about reservoir sampling(method for selecting random sample out of some data), but cannot understand a few things about probability I came across. The article at blog, says that if I'm ...