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

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2
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0answers
58 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. ...
1
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0answers
33 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
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1answer
80 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
49 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
23 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 ...
1
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1answer
29 views

linear dependncy of a random vector with respect to a reduced row echelon form in a finite field

Given a matrix with elements from a finite field $\mathbb{F}_q$, $A\in\mathbb{F}_q^{N\times M}$, where $q$ is the size of the field, $N<M$. Suppose that $A$ in the reduced row echelon form. ...
0
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0answers
25 views

Chaoticity and randomness in a time series

Suppose we have a time series : $X=\{X_t,t\in T\}$. How can we check if the data $X_t$ are random or they are the result of some chaotic behaviour of a nonlinear dynamical system? Is there some test ...
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0answers
52 views

Packing a larger sphere with smaller spheres in high dimensions

We were discussing today the probability of leaving a point uncovered while trying to fill a larger sphere by randomly throwing in smaller spheres. Here's the argument: We are working in ...
1
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4answers
99 views

What is an example for an algorithm which makes use the power of randomness?

Can someone give a (most simple) example for an algorithm on a machine, which has access to random numbers, and which is faster than any other known algorithm for the same task? My actual motivation ...
1
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2answers
68 views

Find the probability of two random real numbers $x$ and $y$ between $0$ and $2$, where $\min(x,y) < 2/3$

Here is a picture of what I did so far. http://sdrv.ms/HhxIvu I got a result of $\frac59$, because the total area is $4$, and I'm subtracting the square with side of $\frac43$. Can anyone confirm ...
0
votes
1answer
58 views

create random random whose sum is constant

Given N numbers. How can I decompose each element x in N into random values r1,r2,..rk (k can be a variable) such that the their sum is equal to x. What can we do if the rs are integers or irrationals ...
1
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1answer
81 views

Searching for random items in a set of lists

This is a programming question, but I'm interested in the math behind it so I think it's better asked here. Say I have a list of items and I'm looking for one item in the list that satisfies a ...
2
votes
0answers
130 views

Finding functions where the increase over a random interval is Poisson distributed

I'm trying to construct a type of function $f(t_1, t_2)$ that counts the number of deterministically simulated Poisson events between two points in time. We can use a single valued function ...
2
votes
1answer
184 views

Triangle Point Picking in 3D

To take random uniform points inside a triangle Triangle Point Picking method is used. But this is for 2D points, how can I take random points from a triangle that is defined by 3 arbitrary 3D points? ...
0
votes
1answer
42 views

Given a Sum, How to Randomly Generate Variables

I have five variables: A=2 B=3 C=4 D=5 E=6 I want to create a random array of these variables so that their sum equals a given number X. Example if X=21, a ...
2
votes
0answers
89 views

How to generate a random matrix which have given singular values?

I know one method: generate a random matrix, apply SVD decomposition, modify singular values, and then multiply those matrices back together. However, I'm wondering how random this method is. Since ...
1
vote
1answer
138 views

number of steps a random walk in a line on the nonnegative integers

let $T_n$ denote the number of steps a linear random walk on the nonnegative integers takes before reaching the position $n$ for the first time. What will be $\mathbb{E}[T_n]$. I tried to derive ...
0
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1answer
38 views

Prove that this is a legitimate PMF

I know that these are two properties of PMF. Non-negativity Sum over the support equals 1 However I can't show that this PMF's sum over the support equals 1.
0
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1answer
74 views

Construction of a random probability measure on the positive integers

Let $\mathcal{N} = \{1, 2, \ldots\}$ be the set of positive integers and let $\mathcal{F}$ be the $\sigma$-field of all subsets of $\mathcal{N}$. Let $X$ be a random variable taking values in ...
0
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3answers
109 views

How to discourage contestants from entering a lottery twice?

Suppose you have a lottery. And you want to prevent participants from buying multiple tickets. What would be the best way to discourage this? For example, increasing the win-chance for all previously ...
1
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1answer
57 views

probability of sequence of random variables

We're going to look at a random process, which is a sequence of random variables that depends on time. Let $X(t)$ = $A/t$ where A has the density $f_A(a)$ = $3/8$ $a^2$ for $ 0<=a <= 2$. Assume ...
1
vote
1answer
94 views

Is there a way to mathematically describe “surprise”?

Let's say that there are ten people entered into a random drawing, the winner gets some large prize. If I were one of those ten people, and I were to win, then I would be pleasantly surprised. If ...
1
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1answer
112 views

Finding the joint distribution of a random process with memory

I'm modeling a digital system as a random process and attempting to solve for the autocorrelation in order to arrive at the power spectral density of the process. The system is as follows: At any ...
1
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1answer
875 views

Probability density of Continuous uniform distribution over the unit circle

If we want to chose a point $(x,y)$ uniformly at random from a unit circle in a plane, why is the joint probability density of the random variable $f(x,y) = \frac{1}{\pi}$ for $x^2+y^2\leq1$? The ...
1
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0answers
42 views

Random Walk in confined region and loop configurations

Suppose I take a random walk on a 2 dimensional square lattice, but this lattice plane has a finite size, e.g. Dx*Dy. I can not cross the boundary, my step length is the lattice cell size, I either go ...
1
vote
1answer
200 views

problem on random variable in probability

A game consists of first rolling an ordinary 6-sided die once and then tossing a fair coin once. The score, which consist of adding the number of spots showing on the die to the number of heads ...
0
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1answer
37 views

Project on generating random numbers on GPU

I have been assigned a project on generating random numbers (specifically lognormal random numbers) on gpu. I have knowledge of probability and statistics and some programming experience but I do not ...
2
votes
2answers
162 views

How to efficiently generate a sequence of random integers that adds up to 1?

I want to randomly generate a sequence of 10 integers in the range [-2, 2] that add up to 1. The distribution of the outcome isn't important. I just want the sequence to be random and the sum ...
1
vote
2answers
286 views

Creating Custom Random Number Generator

My statistics are rusty, but here's what I'm trying to do. Creating an application around football and have this distribution around rushing yards per attempt. ...
2
votes
1answer
69 views

nonlinear transform of Gaussian random variable that preserves Gaussianity

I recently know that following results. suppose that $x_1, x_2, x_3$ are independent real Gaussian random variables with $\mathcal{N}(0, 1)$. Then $$ \frac{x_1 + x_2 x_3}{\sqrt{1+x_3^2}} \sim ...
1
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0answers
43 views

Are there algorithms related to cloud shapes?

This is going to be applied in programming, but I thought the question would be best answered here, since I'm just looking for algorithms at the moment. I'm generating clouds on the fly, but I'm not ...
0
votes
2answers
43 views

Generating a random number of higher range

I had a discussion with my friend about writing a function (a computer program) which generates 9 values randomly using a random number generator which generates 4 values, i.e I have a PRNG rand(4) ...
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0answers
90 views

Nontransitive dice

Here is an introduction to nontransitive dice. The question is: given $n$-player with a $m$-sided dice each one, the what is the minimum of $m$ for a fixed $n$ to produce nontransitivity? Here is ...
2
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3answers
369 views

Random number generator with discrete probability distribution

Is there a general algorithm for implementing a PRNG with a probability distribution?
0
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0answers
111 views

Variance of the first return time of a simple random walk on an hypercube graph

I am trying to solve this problem.... I have a simple random walk on a $d$-cube (finite graph). At each vertex of the graph, the particle chooses one of $d$ edges equally likely. I need to calculate ...
0
votes
1answer
49 views

Probability of random vector lying on a hyperplane

I have a random vector $v \in \mathbb R^n$, of which the elements are independent. Now there is also a hyperplane $S \subseteq \mathbb R^n$ of dimension $n-1$. The vector is drawn from any continuous ...
2
votes
1answer
174 views

Average number of bins occupied when throwing $n$ balls into $N$ bins

There are $n$ balls and $N$ bins. At each time, a ball is thrown in one bin of $N$ bins at random. This repeats n times. So that in total $n$ balls are thrown into bins. The question is, on average, ...
1
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0answers
85 views

Bayesian random walk

Suppose that, at first, I am trying to estimate the mean and standard deviation of some data that I assume to be normally distributed. My prior is gaussian with mean $\mu_0$ and variance $\sigma^2_0$. ...
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3answers
2k views

Normalizing a Gaussian Distribution

Assuming a Gaussian distribution with mean of zero and standard deviation of one, I would like to normalize this for an arbitrary mean and standard deviation. I know you're supposed to add the mean ...
1
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1answer
232 views

Normal distributed rotation matrix in 3D

How can I compute normally distributed 3D rotation matrices with Mathematica? For 2D matrices I would sample a normal distributed angle and directly create a rotation matrix with: ...
1
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1answer
113 views

generating a random periodic function with bounded amplitude and bounded fourier coefficients

I would like to generate (i.e. repeatedly compute via a computer) a random periodic function $f(x)$ with period $T$ such that $|f(x)| \leq M$ and the kth Fourier coefficient $|A_k| \leq g(k)$ for a ...
0
votes
0answers
34 views

Slicing Up Uniform Random Rotation Quaternions

I'm generating uniform random rotations using quaternions. I am using the method attributed to Shoemake, which is discussed in another post (Uniform Random Quaternion In a restricted angle range): ...
0
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1answer
40 views

Would this method yield a truly random sequence?

A creates some content A, say a poem. He assigns an arbitrary number value to each letter of the alphabet. He then selects a random piece of content B somewhere on the web without analyzing it. The ...
9
votes
0answers
187 views

Does $\pi$ satisfy the law of the iterated logarithm?

It is widely conjectured that $\pi$ is normal in base $2$. But what about the law of the iterated logarithm? Namely, if $x_n$ is the $n$th binary digit of $\pi$, does it seem likely (from ...
0
votes
1answer
96 views

Probability of Specific event occuring between 2 events?

Forgive me beforehand for what may be a question with an obvious seolution, but I havent had statistics courses in quite some time. I have an Excel File of approximately 3000 Events, each event has a ...
2
votes
1answer
64 views

A philosophical question on randomness

I have read in some book the following "philosophical" statement : "Introducing randomness we can make unstable things stable". Is there any practical example of this statement.
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0answers
43 views

generating random number with a watch

I don't know if this is the right place to post this question. If not I will move the question with no problem. Does exists an algorithm to generate uniform distributed random numbers using a watch? I ...
3
votes
1answer
106 views

Probability sequential terms of a linear congruential generator are coprime

I was following section 3.1.2 of the Structure and Interpretation of Computer Programming where they calculate $\pi$ using Cesàro's theorem that the probability two randomly chosen numbers are coprime ...
0
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1answer
56 views

Expected length of the “greedy” increasing sub-sequence?

Given a sequence of random unique integers of length $n$, if I select every element that is the largest so far how how many elements should I expect to select? This seems superficially similar to ...
1
vote
1answer
102 views

Yahtzee Bar Game

A bar near where I work has a game where you pay $5$ dollars which gets you two chances of rolling $5$ dice and if roll results in all of the dice having the same number you win the running pot, ...