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

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Probability of single digits from coin tosses

Let's say that I wanted to generate 4 random numbers using a coin toss. I could toss the (unbiased) coin 4 times to generate one of 16 possible numbers (e.g. TTHH=0011=3) and just ignore any results ...
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0answers
13 views

Why are the Real and Imaginary parts of a field in k-space uncorrelated?

I am in the process of generating a (real) Gaussian random field $\delta(\vec{x})$ from a given power spectrum $P(k)$. The way I define the power spectrum is, in Fourier space, $\left\langle ...
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0answers
14 views

Select a random edge [on hold]

Given a source of random bits and a multigraph G(V, E), provide an algorithm for selecting an edge e ∈ E uniformly at random in O(n) time.
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0answers
33 views

Generating a Random Connected Graph

Given a graph G(V, E), with |V | = n and |E| = 0 (that is, the graph is empty), and a static set F containing all the possible edges. Consider the following algorithm for generating a random graph. ...
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1answer
27 views

uniform distribution vs normal distribution for discount use case [closed]

Problem statement: Reward a customer with lucky draw coupon of X% discount in between 1% to 100% Assume that slabs are pre-defined ( all are theoretical) 1% discount : 90% customers 10% ...
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1answer
38 views

LCM of randomly selected integers

What is the expected LCM of 21 randomly selected positive integers under 10000000? How would someone even approach this problem? EDIT: The positive integers are chosen with replacement.
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1answer
21 views

Is $a+r \cdot b$ an uniformly random value when $a,b$ are fixed and $r$ is random value?

Imagine we have two fixed values $a,b \in \mathbb{Z}_p$ and a uniformly random value $r\leftarrow \mathbb{Z}_p$, for large prime number $p$. Question: Is $v=a+b\cdot r$ an uniformly random value in ...
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0answers
11 views

the meaning of 4-wise hash function

If someone says: 4-wise independent sign (hash) functions $s_1,s_2, s_3 : [d] → \{+1, −1\}$, then what does it means? I cannot use k-wise Independence variables (the definition 1 ...
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1answer
32 views

Probability of 2 integers selected are the same is greater than 0.7 in random generated set of 14 intergers. [closed]

A set of 14 random generated integers between (inclusive) 10-30 are generated (repetition is allowed, meaning that it is possible of 2,3 or more random generated integers are same), how many number of ...
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2answers
41 views

What is the probability that at least one 10 day period contains 6 birthdays if there are 60 birthdays throughout a year?

For all possible contiguous 10 day periods within a single calendar year, what is the probability that at least one of the 10 day periods contains six birthdays if there are 60 birthdays randomly ...
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1answer
21 views

Nonlinear transform of two random variables for Gaussianity

I would like to understand the nonlinear transform of Gaussian random variable that preserves Gaussianity better when there is no $x_3$ term such that there exists a nonlinear relationship between ...
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0answers
31 views

mathematical expression for randomely selecting from two integers

I want wondering what is the shortest and correct mathematical expression for the below: $x =$ random$(1$ or $2)$ where there is equal probability of selecting 1 or 2. Thanks for your help.
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0answers
18 views

mathematical notation for random selection of two integers

I want the shortest mathematical notation for the below: $x =$ random$(1,2)$ where there is equal probability of selecting 1 or 2. is it correct to state: $x \sim$ U$(\{1,2\})$. If I had more ...
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1answer
65 views

Partially Identical Hands in Hold'em

I was playing Texas Hold'em at a local cardroom last night keeping a meticulous record of the hands I was dealt. Perhaps I am totally wrong but I thought the occurrences of certain events in this ...
3
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0answers
46 views

independence of x/y and y given that x and y are not independent [closed]

Suppose two non-negative random variates x and y are NOT independent (in my case that I am interested in, the range of x is constrained by y, i.e., $0<x\leq y$). In more specific, assuming $y$ ...
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2answers
34 views

Choosing something 35% more often

If I want to select an element from an array at random, the following will choose each element roughly at 1/L percent of the time: ...
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1answer
45 views

Stat: Probability to have one element of a combination identical to one element of another combination

For a business application, I currently have to provide the probability we are going to have an issue in one application. The combination is composed of N unique ...
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1answer
19 views

Apportioning 100% across 24 hours

Assume I have value x=500. I would like to apportion this value 500 across 24 hours time period and would like it to be apportioned randomly. So if 500 is 100% the x% generated at random would be used ...
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0answers
27 views

Is the Library of Babel random? Does it contain information?

The Library of Babel is defined as a universe in the form of a vast library containing all possible 410-page books of a certain format and character set. However, applying two means of ...
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0answers
12 views

Convergence random matrix inverse

I have the following problem: A is a sum of independent random matrices that converges in expectation to say a matrix C and B is some fixed positive (semi-)definite matrix. I'm interested in a bound ...
2
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3answers
37 views

Expected amount of repeats in a random sequence of integers

I'm looking at a series of random integers generated by a CSPRNG and noticed that there are more repeats (that is a number is in the sequence 2 or more times e.g. 9,3,8,5,6,3 - 3 is a repeat) than I ...
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3answers
68 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
20 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 ...
2
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1answer
36 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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2answers
41 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
48 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
41 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
16 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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0answers
28 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
15 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
70 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 ...
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0answers
80 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
20 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
51 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
29 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
61 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
44 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
12 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
62 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
11 views

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
66 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
15 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
46 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
14 views

Linear congruential generator, $\pmod p$ a prime

I'm interested in pseudorandom generators of the kind $$ x_n = a\cdot x_{n-1} + c \pmod m $$ where $m$ is prime (for concurrency reasons). However, the ones I have found in the literature either have ...
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1answer
34 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
23 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
14 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 ...