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

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0answers
15 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
136 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
33 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
88 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
14 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
32 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
72 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
88 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
93 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
13 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
38 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
51 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
18 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
148 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
47 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 ...
3
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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
23 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
24 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 ...
0
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1answer
55 views

if the probability a shooter hits the target is equal to .8 then …?

if the probability a shooter hits the target is equal to .8 then the probability that the shooter will correctly hit the target after 10 failed attempt is equal ......? probability of hitting the ...
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2answers
37 views

Expectation over multiple variable?

So I have come across a question asked by my peers. Define: $$g:=\sqrt{E[|y_r(t)|^2]}$$ Given that $$y_r(t)=\sqrt{t}\cdot h+k,$$ where $h$ and $k$ are independent random variables with variance ...
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1answer
23 views

The relation between the entropy of random variables $X$ and $Y=g(X)$

A previous post has shown that for random variables $X$ and $Y=bX$, where $b > 0$, the entropy of $X$ and $Y$ are not equal (Entropy of $Y=bX$). However, wouldn't any bijection $g$ on a random ...
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0answers
67 views

How to best randomly shuffle DNA sequence

I seek some help with how best to randomly shuffle DNA sequences. I have a long DNA sequence (lets say 100MB long = 10^8 letters) Using a 3rd party software tool, I am looking for a certain feature ...
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0answers
29 views

How many shuffles are really needed for bridge?

According to the Gilbert-Shannon-Reeds model (which apparently models reality well), one should riffle shuffle seven times to achieve a suitably randomized $52$ card deck. However, it occurs to me ...
23
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5answers
5k views

Method of generating random numbers that sum to 100 - is this truly random?

I am writing a computer program that involves generating 4 random numbers, a, b, c, and d, the sum of which should equal 100. Here is the method I first came up with to achieve that goal, in ...
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0answers
24 views

Modifying a generator of random numbers from a trapezoidal distribution to include growth and decay rates

I've written a C# random number generator based on page 11 of this paper: http://pubs.usgs.gov/tm/04/c03/tm4-C3_final_508_files/tm4-C3_apdx1_v030813.pdf It works fine but I would like to modify it, ...
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1answer
61 views

Generating a random num from a triangular distribution [duplicate]

http://en.wikipedia.org/wiki/Triangular_distribution#cite_note-1 under "Generating Triangular-distributed random variates" given that U is a number between 0 and 1, what happens if the a, b and c ...
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1answer
34 views

(Random Sampling + Approximate Probability + Normal Approximation)

Suppose that 16% of the population of the U.S. is left-handed. If a random sample of 130 people from the U.S. is chosen, approximate the probability that at least 20 are left-handed. Use the normal ...
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0answers
24 views

How would one generate a set of $x$ random values conforming to a certain criteria?

I basically want to generate a set of $x$ numbers given $x$, a minimum, maximum and average. The set of numbers must conform, yielding the given average, with the smallest number being the given ...
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1answer
54 views

Generate random number based on a certain pattern and able to test against the pattern

I have very little idea about random numbers and patterns, so I am not sure whether this is actually possible or not. I want to generate random numbers, that will follow a fixed pattern (perhaps this ...
6
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1answer
105 views

What is a formal definition of 'randomness'?

What is a rigorous mathematical/logical definition of 'randomness'? Under what conditions can we truthfully apply the predicate 'is random'?
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2answers
53 views

Why is the max of x modulo m m-1?

For a sixth grade science project I asked how to scale the following formula: $X_{n+1} = (a X_n + b)\, \textrm{mod}\, m$ And in the answer (Which did work) They said that x generates whole numbers ...
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1answer
35 views

Let $X$ and $Y$ be two uniformly distributed random variables on $[0,1]$. Find $E(X^k)$ and $E(XY^k)$.

Let $X$ and $Y$ be two uniformly distributed random variables on $[0,1]$. Find $E(X^k)$ and $E(XY^k)$. How can you do this? Do you need the change of variables technique? I am a bit confused about ...
2
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1answer
30 views

Random number generator from a piecewise PDF

I'm trying to create a random number generator on the interval $(a,c)$ given a probability density function defined as: $$f(x) = \left\{ \begin{array}{lr} \dfrac{C}{x} &, x \in (a,b)\\ ...
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1answer
81 views

probability, random walk, Markov chain question

Let $P$ be a transition matrix for a regular Markov chain and let $w$ be it’s equilibrium vector. Show that $w$ has no zero entries.
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0answers
23 views

correlation between minimum singular values of submatrices

I have one question regarding how to measure the correlation between minimum singular values of submatrices extracted from a large random matrix. Given a m*n random matrix $\mathbf{A}$, the ...
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0answers
59 views

Approximation for Coupon Collector Probability

I was calculating the probability to draw all items in a list of N items, by picking one randomly, replacing it in the list, etc. (Edit: It's the Coupon collector Problem) I found this formula after ...
4
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1answer
106 views

Rectangle randomly thrown on chessboard

) I'm an electrical engineer and having a tough problem with... math :) geometry and probability... Here's the problem : We have an infinite chessboard. Each square of the chessboard is of known ...
5
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2answers
135 views

Do you need true randomness to beat the two-envelope game?

A well-known (non-)paradox in probability involves a two-envelope game played between two players, $A$ and $B$: $A$ selects two distinct (real) numbers, $x$ and $y$, writing each one down on a card ...
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0answers
22 views

When is a coupling ''natural''?

The definition of coupling is written below. In some articles, I found the term "natural coupling". When is a coupling said to be ''natural''? Definition of coupling between two random variables: Let ...
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3answers
98 views

How to scale a random integer in $[A,B]$ and produce a random integer in $[C,D]$

I know there are many methods to scale a number from range $[A,B]$ to a range $[C,D]$, and I've searched over and over the web. I've seen this math.SE thread. I need to scale a big number (signed ...
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1answer
44 views

Variance and Expected value of internet connection

I am working on a probability/statistics problem! The problem is as follows: Your internet connection is very poor. It constantly alternates between being functional for x minutes and being down for ...
2
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1answer
138 views

Fast method to pick unique random numbers?

In general, computer simulation involving random numbers (lets say to simulate a fair deck of playing cards so $1$ thru $52$) runs fast if you only pick a few cards. However, as you pick more and ...
2
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3answers
54 views

How to handle dice probability? ie, how much more likely would 3 six sided dice give a higher sum than 3 four sided dice?

I am playing at making my own table-top gaming system/rules and I wanted to have a better handle on how likely different dice combinations will give a higher result than one another. I know that a six ...
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2answers
99 views

What are some fast ways to generate random numbers?

Many programming languages come with a function to give random numbers. I wonder how they implement that. Also, assuming the language doesn't have a random function, is there a way to generate them ...
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2answers
35 views

Probability of n random numbers under a threshold

If we choose N random numbers between 0 and 1 (uniformly distributed), what is the probability that at least n will be under some threshold t? For example I want to know if I have a list of 1,000,000 ...
0
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1answer
21 views

A low-discrepancy or quasirandom series which would guarantee all value sequences

I am trying to find a type of quasi-random sequence which would guarantee that it could produce all possible sequences of values within the possible value range, while still producing random-seeming ...
4
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1answer
91 views

Mathematically what are random numbers?

One topic in mathematics and computer science that always confused me were random numbers. I tried searching for the exact meaning but it feels kind of abstract and incomplete. Mathematically random ...
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0answers
71 views

Conceptual Understanding of a Simple Random Process

I have a simple discrete time random process that with probability $0.5$ chooses a deterministic sequence so that $X(t) = -1$, for $t<1$ and $X(t) = +1$ for $t \geq 1$, similarly with probability ...