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

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1answer
27 views

Need way to statistic puzzle

Hello guys i need help with statistic problem. The problem is : In room have 3 doors, one door is exit from room (o minutes) , second is return us to the room after 3 minutes , and last door is ...
0
votes
1answer
29 views

Using dieharder to certify randomness of a random sequence

I would like to prove (at a certain level) the randomness of a random sequence of N bits. I know that the dieharder battery of tests is supposed to be used to test the generator, not a particular ...
1
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0answers
17 views

Distribution using the Poisson Point Process model

I need to use the Poisson Point Process (PPP) model to randomly distribute a set of 'objects'; over a given area: Let's say that we have N objects to distribute over an area that has been split ...
3
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0answers
53 views

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 ...
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0answers
23 views

bounding absolute fluctuations of random variable distribution

I have a discrete random variable with values $\underline{y} = (y_1, y_2, \dots , y_d)$ with corresponding probabilities $\underline{x} = (x_1, x_2, \dots , x_d)$ and average $Y = \sum_i x_i y_i$. ...
1
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1answer
53 views

Logic behind Metropolis algorithm

I am using Metropolis algorithm to make a program for Ising model in Statistical Physics. In Ising model, we take a collection of spins with initial energy, say $E_i$, then we randomly flip one of the ...
1
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1answer
29 views

Is there a way to generate this class of bivariate distributions from two uniform random variables?

I need to generate a pair of random variables $U,V$ with distribution $$ f_{U,V}(u,v)\propto(u+v)^{-4} $$ in $u,v\in[1,L]$ with $L>1$. I managed to invert the CDF of the marginal distribution for ...
0
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1answer
61 views

What is the difference between Discrete and Continuous Random Variables?

What is the difference between Discrete and Continuous Random Variables? Discrete Random Variable = takes countable or discretely determinable values. So, it is always listable. For example, digital ...
2
votes
2answers
43 views

Why a shuffling algorithm is not uniformly random between [1, N)? [closed]

I've been taught that simple shuffle algorithm will not be uniformly random if the interval for the random numbers is not [1, N), i.e. it can't be from 0 to N, it must be from 1 to N-1. I'm trying ...
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2answers
91 views

Continuous Random Variable question, Probability and Statistics

a little help please A couple decide they really want a daughter. So, they decide to start having children and continue until they have their first daughter. Assuming having either a boy or girl is ...
1
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1answer
50 views

Convergence of sequence of random variables to infinity

Suppose $X=X(\alpha)$ is a sequence of non-negative continuous random variables indexed by a continuous parameter $\alpha$ such that $\alpha$ is in $[0,\alpha_0)$ for some finite positive $\alpha_0$....
1
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1answer
70 views

Random but very interesting probability question! [duplicate]

There are 100 types of cards, each type with a number from 1 to 100 on it. Each minute I am given a random card. Random means that the number of my card has an equal chance of being 1,2,3,...,100. I ...
1
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1answer
67 views

Wiener Process definition - Continuous paths?

A stochastic process $\{W(t): t \in T\}$ is a Wiener process if it satisfies the following properties: 1) $W(0)=0$ with probability $1$ 2) It has stationary and independent increments. 3) For every ...
0
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1answer
45 views

How do multiple trials affect certainty?

Suppose you have two coins: one is a normal coin (with one "heads" side and one "tails" side), and the other is a modified coin with two "heads" sides. The coins are indistinguishable apart from ...
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0answers
18 views

Permutations for a linguistics project

I am going to have subjects read the following word lists: English A English B English C Spanish A Spanish B Spanish C I always want the subjects to alternate between reading English lists and ...
1
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0answers
104 views

Invertible pseudo random number generator

I want to create a random sequence using a given seed. However when given a sequence I also want to calculate the seed which produces the sequence. Of course this is not possible using a "true" ...
-1
votes
1answer
59 views

Show that if $(X_1,Y_1)$ and $(X_2,Y_2)$ are independent random vectors, then $(X_1,Y_1,g(X_1,Y_1))$ and $(X_2,Y_2,g(X_2,Y_2))$ are as well.

I am not sure how to go about showing that $(X_1,Y_1)$ and $(X_2,Y_2)$ being iid implies that $(X_1,Y_1,g(X_1,Y_1))$ and $(X_2,Y_2,g(X_2,Y_2))$ are iid for any measurable function $g:R^2\rightarrow R$....
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4answers
289 views

Random irrational number generator?

Is it possible to create a algorithm that will generate irrational numbers $0<x<1$ with a density that is uniform down a specified resolution? Would such an algorithm be necessarily limited to ...
0
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0answers
62 views

How to draw lots in a group of people without duplicates and not all present

I have a problem that certainly has some mathematical solution. The problem: In a group everybody writes his/her name on a paper, puts it in a bowl and everybody draws a paper. If someone draws his/...
1
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0answers
46 views

How to approximate damped harmonic under random forcing

Given motion in response to random forcing, can a "simple" function be used to estimate future motion. Starting with the damped harmonic oscillator, we can write $${d^2 \over {dt^2}} h(t) + 2 \zeta \...
3
votes
3answers
83 views

Probability doubles if you switch cards when the third card is revealed, How? [duplicate]

So I was watching the show Numb3rs, and the math genius was teaching, and something he did just stumped me. He was asking his class (more specifically a student) on which of the three cards is the ...
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0answers
46 views

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 ...
0
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1answer
45 views

Finding the average cluster size of a random grid

Original problem statement: Melon-boy lives in a flat world, where there is an infinite two-dimensional grid, where each gridsquare is either occupied by a melon (50% chance) or a pumpkin (50% ...
1
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2answers
36 views

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
18 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 \delta(\...
6
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0answers
98 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. ...
0
votes
1answer
60 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% ...
-1
votes
1answer
53 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.
2
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1answer
42 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 $\...
1
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0answers
22 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 http://www.math....
1
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2answers
57 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 ...
0
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1answer
49 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 $...
1
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0answers
45 views

Mathematical expression for randomly selecting from two integers

I wonder 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.
0
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0answers
26 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 ...
0
votes
1answer
69 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
67 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 $y$ ...
0
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2answers
38 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: ...
0
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1answer
68 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 ...
0
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1answer
51 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 ...
2
votes
1answer
165 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 ...
0
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0answers
84 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
votes
3answers
78 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 ...
2
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3answers
87 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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votes
1answer
24 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
votes
1answer
37 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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3answers
91 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 $x$, $...
2
votes
3answers
61 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 ...
1
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1answer
91 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 ...
0
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0answers
53 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. ...
3
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0answers
51 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 0)\...