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

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1answer
54 views

How to Create a Plane Inside A Cube

I have a $e \times e \times e$ cube and I want to create random planes with equation $ax + by + cz + d = 0$ inside this cube. I will put random points on those randomly created planes as well. Here ...
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2answers
68 views

Consider throwing two six-sided dice.

Let X be the sum of the two values and let Y be the product of the two values. What is the value of P(Y = i) for i = 1,2,3...36. I am having trouble approaching this problem. We are learning about ...
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1answer
109 views

Solution of equation of binomial random variables

Is it possible to find the probability distribution of the random variable $X$ that solves the following equation? $$ X = Bin(X, p) + Bin(X, 1-p), $$ where $Bin(X,p)$ is a random variable distributed ...
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2answers
214 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 $\alpha$ = ...
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1answer
60 views

Probability of occurrence after Latin Hypercube sampling and then random sampling

I am using Latin Hypercube sampling to obtain numbers from a Normally Distributed set of data, so that I get a uniform spread of numbers across the Normal Distribution. I then select a number at ...
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1answer
21 views

Probability of numbers within a Latin Hypercube

What is the probability of occurrence of numbers in a Latin Hypercube? If I have a 1 dimensional Latin Hypercube of 1000 numbers would the probability of each number just be 1/1000? Essentially, I am ...
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1answer
202 views

Generating Different types of Matrices in Matlab

I am working on a project for a numerical methods class comparing two iterative methods for solving $Ax=b$, and I was wondering what type of functions Matlab has for generating arbitrarily large ...
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0answers
63 views

Random walk with $\sum_{n=1}^{\infty} \frac{1}{n} \mathbb{P}\{ S_n > 0 \} < \infty$

Consider a random walk started at $S_0=0$, denoted $S_n = \sum_{k=1}^{n}X_k$, where $X_1$, $X_2$... are the i.i.d increments. If we have $\sum_{n=1}^{\infty} \frac{1}{n} \mathbb{P}\{ S_n > 0 \} ...
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1answer
49 views

Probability of random variable in Normal Distribution

I've been talking to my lecturer about choosing random values from a Normal Distribution and he says the following: "Roughly 68% of expected values $ \in (\mu-\sigma,\mu + \sigma)$ does not imply ...
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1answer
42 views

Randomized algorithm to determine if a polynomial over $\mathbb{Z}/p$ is irreducible

Is there an efficient (possibly randomized) algorithm to determine if a given polynomial $p(x) \in \mathbb{Z}/p\mathbb{Z}[n]$ is irreducible?
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56 views

determining the next random number pseudorandom number generator?

I have given 3 numbers let's say basic example x_0=5, x_1=6 and x_2=2 and modulus p is 7, ...
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0answers
35 views

Random operators [duplicate]

Let $(\Omega, \mathcal F,P)$ be a probability spaces and $H$ be a Hilbert space. By a random operator $A$ from $H$ to $H$ we mean a linear continuous mapping from $H$ into the Frechet space $L_0^H ...
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1answer
54 views

Algorithms for non-random but equidistributed ways to fill up a Cartesian plane

In pages 90-91 of this book the authors talk about uniform, but not necessarily normally distributed random ways to fill up a Cartesian grid. For example, in the attached images. These are the ...
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1answer
87 views

Random walk in nXn grid. probability reaching top row

A woman walks randomly on a nxn grid starting at the point (1,1) (the lower left corner). Each minute the women moves either to the right or up (so (a,b)-> (a+1,b) or (a,b)->(a,b+1). Her walk ends ...
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1answer
58 views

Probability question (grid)

Say I have a grid of 10x7. Every square of that grid is empty. Then, 20 squares, chosen at random, are filled (a square can only be filled once, so no duplicates allowed). What is the probability of ...
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3answers
134 views

Probability of collecting all 5 different items at random with different weights

There are 5 different items in a set, each with a weighted chance of being rolled randomly [A-E]. The weights add up to 100%. $$A=5\%, B=10\%, C=15\%, D=30\%, E=40\%$$ You get 1 item every roll no ...
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0answers
86 views

Random pair generation?

Suppose there are 6000 people, there will be a combination of $$\binom{6000}{2}$$ ways for 2 people to be chosen out. Now the task is to randomly choose 5000 pairs of people in the total 6000 ...
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1answer
164 views

Generating Random Serialnumber with least similarity

I want to generate 16-digits hexadecimal serial-number like: F204-8BE2-17A2-CFF3. (This pattern give me 16^16 distinct serial-number But I don't need all of them as I describe below) I need an idea ...
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1answer
93 views

What is a pdf of Gaussian noise convoluted with a sine wave?

I realize that it is relatively easy to compute the variance of an AWGN convoluted with a sine-wave through auto-correlation function. My question is how do I find the pdf if I know the variance and ...
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1answer
243 views

random number usage in filling 2d array

Below is a small program which has 2-3 Math concepts involved we have 2d array of $i$ width and $j$ height, idea of this program is to fill ...
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2answers
21 views

Show that $Cov(X,Y) \geq -23$

if $X,Y$ are two random variables and: $Var(X) = Var( Y) = 23$ how can i show that $Cov(X,Y)\geq -23$ can someone give me some hints on how to show it?(not an answer) i know that $Cov(X,Y) = E(XY) ...
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2answers
62 views

the maximum of two random variable

The maximum of two random varibles $X$ and $Y$ is: $$Z=\max\{X,Y\}= \begin{cases} X & \text{if } X \geq Y \\ Y & \text{if } Y \geq X \end{cases}$$ I don't understand. So if I roll two dice, ...
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0answers
38 views

Can I solve this probabilistic problem or do I need more data?

This problem happened to me almost 3 years ago and I just discovered this site by luck, so I want some help to know if this problem is solvable (if so, I would like to know how to solve it as well as ...
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17 views

Singular value of random matrix after linear transformation

Let $A$ a $n \times n$ random matrix with i.i.d $N(0,\sigma^2/n)$ entries. Let $H$ an invertible matrix, and denote $\sigma_H$ the largest singular value of $HAH^{-1}$. My question is : in the large ...
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2answers
238 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 ...
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1answer
44 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 ...
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2answers
60 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% ...
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1answer
22 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 ...
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79 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 $y = \frac{x_1 x_2}{ax_1 x_2 + bx_1 + cx_2 + d}$ ...
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1answer
73 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 := ...
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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?
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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 ...
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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 :)
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65 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 ...
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1answer
120 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 ...
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23 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 ...
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1answer
75 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 ...
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1answer
82 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, $$ ...
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2answers
51 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 ...
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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. ...
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0answers
109 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 ...
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3answers
178 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 ...
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36 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?
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1answer
97 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 ...
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3answers
231 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?
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46 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} ...
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56 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, ...
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1answer
99 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 ...
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1answer
66 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 ...
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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 ...