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

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Algorithm to randomly seat groups of guests at tables

I am not a professional in Maths, but the Problem I would like to solve is mathematical in Nature, so I hope this place is right to ask. Please feel free to annotate incorrect definitions, since this ...
2
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3answers
59 views

Can you get a fair coin flip by rolling a fair, 5-sided die a finite number of times?

Can you get a fair coin flip by rolling a fair, 5-sided die a finite number of times?
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1answer
18 views

Which is the probability?

On the Swedish SAT test, you have 5 options for every question where precisely one option is correct. If you answer randomly, what is the probability that your score will be 0.9 if the maximum score ...
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1answer
33 views

Intuition on Martin-Löf-Test for finite strings

The followng example is from An Introduction to Kolmogorov Complexity and Its Applications, Example 2.4.1. and is concerned with Martin-Löf-Tests for finite strings: A string $x_1 x_2 \ldots x_n$ ...
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1answer
29 views

Partition-based entropy of a sequence

The entropy $H$ of a discrete random variable $X$ is defined by $$H(X)=E[I(X)]=\sum_xP(x)I(x)=\sum_xP(x)\log P(x)^{-1}$$ where $x$ are the possible values of $X$, $P(x)$ is the probability of $x$, ...
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3answers
42 views

Intuition behind generating continuous random valiables

If we have a random variable $X$ with cumulative distribution function $F$ that is strictly ascending and we manage to find the inverse we can generate an instance $x_1$ from a uniformly distributed ...
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1answer
38 views

Generate random number according to any equation

So I'm after a random number generator where the probabilities of a number occurring in some range is matched to some function. Only really looking at functions with nice integrals (for simplicity ...
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0answers
14 views

continuous random variable - pth percentile

Let X be a loss random variable with cdf $$ F(x) = \left\{ \begin{array}{ll} 1-(θ/θ+x)^α & \textrm{for $x≥0$}\\ 0 & \textrm{for $x<0$}\\ \end{array} \right. $$ The 10th percentile is θ−k. ...
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23 views

How to sample from a convex hull?

Let us consider a couple of points $x^{(i)}\in \mathbb{R}^m$ where $i=1,\dots,n$. Convex hull is defined as $$ C = \left\{\sum_{i=1}^{m} \alpha_i x^{(i)} \mathrel{\Bigg|} (\forall i: \alpha_i\ge ...
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1answer
30 views

Shuffling the columns of a matrix

Suppose I have an $N\times k$ matrix: $$\begin{bmatrix}a_{1,1} & \cdots & a_{N,1} \\ \vdots & \ddots & \vdots \\ a_{1,k} & \cdots & a_{N,k} \end{bmatrix}$$ Is there a ...
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0answers
13 views

Is two single byte random codes more secure than a single word random code?

I am trying to create secret keys for a post so users can edit them without entering password. Typically I use two secret IDs to reference a post, ID1=8 byte long random code ID2=8 byte ...
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2answers
65 views

A single, good test for a random number generator?

I'm chasing a bug in the RNG for a well-known programming language under certain pathological inputs. There is an obvious pattern in this pathological case, apparent with very small n (~ 10000), and ...
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1answer
30 views

Hitting all bins at least once

$m$ balls are thrown at a total of $n$ bins. Each ball will fall into exactly one randomly chosen bin with each throw. What is the probability that each bin is hit at least once (contains at least one ...
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1answer
22 views

Uniform random number generation

Given a uniform random number generator that generates integers between any given range, a n-tuple $b$, and an integer $c$, how can one uniformly generate n-tuples ($x$) that meet the following ...
6
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0answers
74 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 ...
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0answers
16 views

Function/algorithm to generate a random walk on a graph

I'm looking for a graph function or an algorithm that can generate a random fluctuating random walk that will eventually converge between the value of y = 0 and y = 1, more or less after a number of ...
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1answer
46 views

Randomness in pi and other irrational numbers [duplicate]

This is a post I read about pi while looking for stuff about tau -which is two times as much as pi. This makes me wonder, why does only pi contain such randomness? Don't other non-repeating and ...
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0answers
27 views

A set of conditions to prove or disprove randomness

I am trying to understand the heuristic connection between fitting a normal distribution to a dataset and the definition of what constitutes a random process. If a normal distribution fits your ...
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4answers
56 views

The normal distribution is a common model of randomness

Can someone please comment/elaborate on the statement: "The normal distribution is a common model of randomness." I would like to understand it more deeply. Source: Perhaps someone can point me ...
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2answers
39 views

Worst case binary search

Suppose you play a game with a computer program where you guess a number between 0 and 1 and the computer uses binary search to search for your number. My question is what is the best number to ...
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0answers
10 views

How to define a one-parameter family of probability distributions

I am trying to evaluate a noise-source as a means of providing entropy to a random number generator. I am running into trouble when it comes to determining the probability distribution that has the ...
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2answers
59 views

Random equation-does it make sense?

What is the probability that the equation $$x^2+2bx+c=0$$ has real roots? Answer is exactly $1$. (or $100$%) For example: if $b=1$ and $c=2$ roots are complex. Does it make sense? If $P(A)=0$, then ...
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0answers
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Can PRNGs and RNGs work as different RNG/PRNGs?

I think the title was pretty bad but I'll explain. Let a RNG-n and a PRNG-n be a random integer generator and pseudo-random integer generator respectively that both randomizes integers from 1 to n (1 ...
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2answers
64 views

How many bit-flips are required to achieve random distribution?

If I have a binary number W bits wide, initially all set to zero, and I repeatedly pick a random bit and toggle it from zero to one or vice versa, how many times would I need to do this to achieve ...
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1answer
13 views

Dynamic weighed probability

If I have a list of objects, and want [programmatically] to randomly pull one out, I can simply choose a random number representing a valid index within the range of elements of the list: ...
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2answers
44 views

Can this probability mechanic be used in a simulated gambling scenario?

This question is a bit complicated, so please bear with me. I realized this question after watching this video from the popular Youtube channel Numberphile. This video claims that when two random ...
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0answers
8 views

Linear congruential generator, $\pmod p$ a prime

I'm interested in pseudorandom generators of the kind $$ x_n = a\cdot x_{n-1} + c \pmod n $$ where $n$ is prime (for concurrency reasons). However, the ones I have found in the literature either have ...
2
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1answer
32 views

Unknown random number generator

I recently browsed through someone else's code and found a section where a pseudo random number generator is implemented. I know that random number generation is not an easy task, some even regard as ...
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1answer
22 views

Randomization and probability with constraints

The probability of getting a specific suit out of a deck is 13/52. Once we have one suit (color) selected the probability is 12/51 for that suit and 13/51 for others. This much is obvious. Now ...
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1answer
13 views

Random Numbers and Binomial Distribution

Let's say we have generated n=100000 numbers from a set: {1, 2, ..., 50}. Let X a discrete random variable that expresses the number that 1 appears. Then X~Binomial(n,p), where n=100.000 and p=1/50 ...
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0answers
14 views

Non-linearity on Random Sequence

I recently incorrectly assumed that applying a non-linear operation on a completely uncorrelated sequence would yield an uncorrelated sequence. Turns out that it is trivially easy to show that this ...
7
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3answers
125 views

Random Sequence of Alternating Increase/Decrease Numbers

The problem statement: Repeatedly pick a random number (uniformly-distributed) between $0$ and $1$. Keeping going while the second number is smaller than the first, the third number is larger than the ...
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2answers
32 views

Random 4D vector

I'd like to generate random 4D vectors. Their length must be 1. A random 2D vector can be created like so: ...
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4answers
85 views

What is the statistical equilibrium for this simulation of happy bubbles?

Happy Bubbles I hope this is not too specific or practical, but I just made a simulation of sorts and seem to have hit quite close to an equilibrium (by accident). Now I am wondering if and how you ...
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0answers
12 views

How to find covariance matrix from correlation if mean is not given?

I'm given autocorrelation function of gaussian random process: $$ R_x(\tau) = 3e^{|-\tau/3|} $$ Now I should find covariance matrix. I know the formula and solutions, where $$ C_{xx} = R - E[X]E[Y] $$ ...
2
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1answer
28 views

What was the paper about flower-shaped knots?

I read a article about the possibility to bring knots in a "polar rose" projection, where there is only one crossing of higher multiplicity. The overcrossing/ undercrossing information is thus more ...
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0answers
30 views

a sequence of integers associated to a bernoulli process

Is it possible to associate a sequence of integers to a Bernoulli process such that for every trial an integer is chosen and the average of the integers associated to the successes is twice the ...
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0answers
68 views

Confusion about a random process

Let $X(t)$ be a random process such that: $$ X(t) = \begin{cases} t & \text{with probability } \frac{1}{2} \\ 2-at & \text{with probability } \frac{1}{2} \\ \end{cases}, $$ where $a$ is a ...
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2answers
64 views

Random Uniformly Distributed Points in a Circle

I know that by just using a random angle and a random radius within the bounds of your circle, you will end up with points near the center of a circle. Whereas if you do ...
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1answer
92 views

Variance of a special random walk

I am trying to find the variance of the following special random walk: Suppose that $U=(U_1,U_2,...)$ is a sequence of independent random variables, each taking values $u$ (for up) and $d$ (for down) ...
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1answer
29 views

Suppose that $N$ is an iid geometric RV and $X_i$ is an iid Bernoulli RV. Find the p.g.f. of $R=X_1+ \dots + X_n$.

Each year a tree of a particular type flowers once and produces a random number $N$ of flowers, where $\mathbb{P}(N=n)=(1-p)p^n$, $n=0,1,2,\dots $ and $0<p<1$. Each flower has probability $1/2$ ...
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0answers
11 views

Clarification: Deterministic vs Pseudo- Random Number Generation

I came across the readme for a program stating that it was capable of "Simulation tooling: discrete event simulation and deterministic random number generation." I've never heard of this term used ...
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1answer
36 views

Continuous random variables and probability density function

OK, I know that a random variable $X$ from some probability space to $\mathbb R$, with some additional properties. It is discrete if it's image in $\mathbb R$ is dicrete. It is otherwise called ...
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0answers
44 views

Distinct pairs formed using repeated sequences

Problem setting: Let $N$ and $M$ be positive integers. Let $I'$ and $J'$ be ordered sets, i.e., sequences, $\{1,2,\ldots,N\}$ and $\{1,2,\ldots,M\}$ , respectively. The sequences are $N$ and $M$ in ...
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0answers
17 views

Calculation of arrival time of messages from 1 source through 2 different routes

I need to simulate sending messages from $A$ to $B$ as follows: Each message is sent $N$ times from $A$ on the same time, passes through a certain route $R_n$ and arrives at $B$. Travel time of $R_n$ ...
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1answer
146 views

Generating a random matrix with prescribed conditions

I need to uniformly generate a random matrix $X$ with positive integer entries satisfying a number of prescribed conditions: The matrix dimensions are prescribed, say $m\times n$ For each row, the ...
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1answer
44 views

Testing randomness

I'm looking for informations about randomness and especially - random numbers. I found some about random number generators, but for now, the question, that concerns me is how statistically differ ...
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1answer
49 views

Class of graphs with symmetric random walk

Let $(V,E)$ be a graph and let $X_n$ be a random walk on the graph. At every step, the walker at $x$ jumps to one of the neighbors drawn uniformly at random among all the vertices $y$ such that there ...
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1answer
22 views

Expected Value: how to understand this expression?

So I have come across a question asked by my peers. Define: $$g:=\sqrt{E[|y_r(t)|^2]}$$ Given that $$y_r(t)=\sqrt{t}\cdot h+b+k+c,$$ where $h$, $b$, $k$, and $c$ are independent random variables. ...
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0answers
21 views

How to compute the average power of an ergodic process?

Rxx(0)=3 is the average power and if i take limit as t goes to infinity i will get the (E[x])^2 to get variance you subtract 3-2 = 1 is this correct ? and can someone tell the difference ...