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

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2
votes
0answers
38 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 ...
0
votes
1answer
29 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 ...
0
votes
2answers
86 views

Probability of an interval (A, B) being in (C, D) or vice versa [on hold]

$S$ is the domain. $A, B, C, D \in S$. $A, B, C, D$ satisfy the condition $A \le B$ and $C \le D$ and hence $(A, B)$ and $(C, D)$ form intervals. All four are values picked from respectively $4$ ...
0
votes
1answer
20 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 ...
4
votes
0answers
39 views
+100

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 ...
0
votes
0answers
13 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 ...
1
vote
1answer
42 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 ...
2
votes
0answers
26 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 ...
1
vote
4answers
52 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 ...
0
votes
2answers
37 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 ...
0
votes
0answers
9 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 ...
0
votes
2answers
59 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 ...
0
votes
0answers
8 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 ...
1
vote
2answers
64 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 ...
1
vote
1answer
10 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: ...
2
votes
2answers
41 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 ...
0
votes
0answers
8 views

Linear congruential generator, $\pmod p$ a prime

I'm interested in pseudorandom generators of the kind $$ x_n = a\cdot x_{n-1} + c \pmod n $$ where $n$ is prime (for concurrency reasons). However, the ones I have found in the literature either have ...
2
votes
1answer
29 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 ...
0
votes
1answer
20 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 ...
1
vote
1answer
13 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 ...
1
vote
0answers
14 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
votes
3answers
112 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 ...
0
votes
2answers
32 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: ...
2
votes
4answers
81 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 ...
1
vote
0answers
12 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
votes
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 ...
0
votes
0answers
30 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 ...
0
votes
0answers
65 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 ...
1
vote
2answers
55 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 ...
-3
votes
1answer
92 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) ...
1
vote
1answer
26 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 $1/2$ ...
0
votes
0answers
10 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 ...
1
vote
1answer
25 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 ...
1
vote
0answers
41 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 ...
1
vote
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
votes
1answer
135 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
vote
1answer
40 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
48 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
votes
1answer
22 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. ...
0
votes
0answers
21 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
votes
1answer
29 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 ...
2
votes
2answers
30 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 ...
0
votes
1answer
22 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
votes
0answers
64 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 ...
1
vote
0answers
26 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
votes
5answers
4k 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 ...
0
votes
0answers
16 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
votes
1answer
52 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 ...
0
votes
1answer
22 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
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 ...