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

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2
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1answer
1k views

gap test for random numbers

I'm in process of learning 'gap test' for random numbers in discrete event system simulation. I happened to have the fourth edition of this book by Jerry Banks. Unfortunately , this edition doesn't ...
1
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0answers
15 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 $R_n$ ...
0
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1answer
99 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 ...
1
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0answers
16 views

Return random element from array excluding elements from subarray [migrated]

Basically, I need something like this: f(a[], b[]) = random element from a[] which is not in b[] Idea I have is this one: ...
1
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1answer
33 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
votes
1answer
43 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 ...
0
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1answer
20 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. ...
-3
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0answers
28 views

Connecting random numbers. [closed]

There are n numbers. They are random. One is to come up with an expression which when solved yield these numbers and only these n numbers. Is it possible? The domain is restricted to positive ...
0
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0answers
19 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 ...
19
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4answers
8k views

Picking random points in the volume of sphere with uniform probability

I have a sphere of radius $R_{s}$, and I would like to pick random points in its volume with uniform probability. How can I do so while preventing any sort of clustering around poles or the center of ...
2
votes
2answers
27 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 ...
5
votes
1answer
633 views

Mapping random points on a sphere onto a uniform grid

Say I had an arbitrary sphere that is covered in a uniform triangle mesh of N elements with each element having a unique sequential index. If given the coordinates of a random point on the surface of ...
0
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1answer
19 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 ...
23
votes
6answers
3k 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 ...
1
vote
2answers
326 views

How can I generate a random number on my ti-84 without the rand function

Is there an equation that is possible where I enter a seed, and it will give me the number from the seed. I want it to give me the same results as the rand function would give with the seed as 0. I ...
2
votes
1answer
318 views

Fast generation of Pareto-distributed randoms.

I'm developing a library of routines for generating random numbers for simulations (it's on GitHub). I've included fast routines for normally distributed and exponentially distributed randoms, using ...
0
votes
1answer
19 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 ...
0
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0answers
56 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 ...
0
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1answer
44 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 ...
1
vote
1answer
251 views

Compressing random numbers

I've been thinking about ways to compress the output from a (supposedly) random number generator. Let's assume for a moment that my computer can produce high-quality random numbers. I'm certainly not ...
1
vote
1answer
14 views

How random are numbers from geometric distribution

If I will choose a value $r$ as a random number from uniform distribution, I can be sure, that this value is totally random - because each value is equiprobable. However, what if I will take a value ...
1
vote
0answers
24 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 ...
0
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0answers
11 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, ...
-1
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1answer
40 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 ...
5
votes
2answers
909 views

Random number generation inside an interval based on cdf (Zipf and Exponential)

Consider for example the Exponential distribution with c.d.f. $F(x) = 1-e^{-\lambda x}$. $F^{-1}(x)$ would be inverse cdf (quantile function). If I generate y=F−1(x) with x uniformily distributed on ...
0
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0answers
18 views

Power spectral density

Please help can someone help me with these. Any help is accepted. Thanks
2
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3answers
589 views

How to compare randomness of two sets of data?

Given two sets of random numbers, is it possible to say that one set of random numbers has a greater degree of randomness when compared to the other? Or one set of numbers is more random when compared ...
2
votes
2answers
1k views

What does relaxing the iid assumptions mean? Intuitive and technical perspectives.

I believe the most restrictive assumption we can place on a series of observations is that they are iid. It is possible to relax these assumptions. For example relaxing the independent distribution ...
0
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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 ...
0
votes
1answer
20 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 ...
0
votes
1answer
14 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 ...
0
votes
2answers
44 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 ...
4
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0answers
46 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'?
3
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2answers
607 views

Can random number generators be used in compression?

This is basically a recurring thought I have from time to time and I suspect it is flawed, so my question is basically why can't you do the following: Basically, I imagine that given a seed and a ...
1
vote
1answer
28 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
votes
1answer
24 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)\\ ...
6
votes
2answers
1k views

What is golden ratio doing in this computer code?

In this file (related to random number generation), there is following line: private const int MSEED = 161803398; which resembles golden ratio. How come ...
0
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0answers
47 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 ...
141
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25answers
10k views

Can a coin with an unknown bias be treated as fair?

This morning, I wanted to flip a coin to make a decision but no coins were in reach. There was however an SD card on my desk: Given that I don't know the bias of this SD card, would flipping it be ...
0
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1answer
72 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
13 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 ...
0
votes
2answers
46 views

How to decide the randomness of a dataset by checking the prime numbers inside it?

So it is weekend! I am reading currently a book where I found this sentence: "71 percent of men said they had a 'good sense of direction'. Only 47 percent of women reported same thing.", and I thought ...
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0answers
33 views

How many different random numbers can you generate between zero and infinity?

My theory is that you can't generate any random number between zero and infinity. But thats kind of unexpected because you can generate 100 different random numbers between 0 and 100 and 1000 ...
4
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1answer
95 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 ...
4
votes
1answer
82 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 ...
2
votes
1answer
118 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 ...
4
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3answers
81 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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0answers
21 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 ...
0
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1answer
41 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
votes
1answer
79 views

Cross Power Spectral Density from Individual Power Spectral Densities

Let $X$ and $Y$ be two zero-mean, wide-sense stationary random processes. The power spectral density of a process is the Fourier transform of the process's auto-correlation function. The cross power ...