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

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3
votes
1answer
471 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 ...
-1
votes
2answers
34 views

What random variable is this?

I have a sequence of reals $S = s_1,s_2,\dots,s_n$ such that $s_i-s_{i-1}$ is a Gaussian distribution. From histogram of sequence $S$ (10000 elements) it appears that it is uniform distribution. Is it ...
1
vote
1answer
46 views

Attempt to solve a matrix (counterbalancing) problem computationally gives “spooky” result: why?

This question is posted on the mathematics section of stackexchange because my uneducated guess is that the answer involves some basic mathematical principles, possibly in the domain of linear ...
0
votes
0answers
12 views

Prove that the mean of the $u_i$'s generated by a congruential linear generator of complete period is $\frac{1}{2} -\frac{1}{2m}$

Congruential linear generator (pseudo random numbers) I have to prove this proposition but I don't know how. I tried by induction on $m$, the modulus of the generator, but it hadn't got me anywhere: ...
1
vote
1answer
42 views

Ms. A selects a number $X$ randomly from the uniform distribution on $[0, 1]$. Then Mr. B repeatedly, and independently, draws numbers. [on hold]

Ms. A selects a number $X$ randomly from the uniform distribution on $[0, 1]$. Then Mr. B repeatedly, and independently, draws numbers $Y_1, Y_2, ...$ from the uniform distribution on $[0, 1]$, until ...
0
votes
1answer
20 views

Random sum of normal distribution with bounds Poisson distributed?

A random variable, $M$, is Poisson distributed with $\lambda=2$. ${X_1,X_2,\dots}$ are independently identically distributed random variables with $\mu=3$ and $\sigma=.2$. Introduce a new random ...
-1
votes
2answers
45 views

Empirical Process estimation using gaussian density and specific random generator

EDITED: To formulate into math framework: I have a sampling generator producing IID gaussian. To highlight the convergence in the distribution, I calculate the following error. Given a precision ...
0
votes
0answers
15 views

Is there any trick for evaluate this integral?

Does the following function can be simplified or solved? $$R(i) = \int_{y\in S} {\frac{{w(y) g(y,i)_{}^\sigma }}{{\int_{x\in S} {h(x)g(x,y)_{}^\sigma f(x,y)_{}^\sigma dx} }}dy} $$ where S is a ...
1
vote
2answers
39 views

Calculating first and second moments for random sums?

Assume that $N$ and $X_1, X_2, \ldots $ are all independent and identically distributed over $(0,1)$ with the density function: $f (x) = cx^2 (1 − x)^2$. An integer–valued random variable, $N$ ...
0
votes
0answers
8 views

Statistical distance between a multiplicative mask and a random number

Given $x \in \{1,\ldots,2^n\}$ and a uniform random $r \in \{1,\ldots,2^{n+k}\}$, then the statistical distance $\Delta(x + r\bmod q; r) < 2^{-k}$, for a $q > 2^{n+k+1}$. With addition this is ...
0
votes
2answers
28 views

What is the probability or percentage or frequency by which hello line will be printed?

I have a below method which is called every one minute from background thread and that background thread keeps running always. ...
1
vote
2answers
129 views

Understanding Sobol sequences

Can someone explain to me in simple terms, how Sobol sequences work? The wikipedia article is fairly technical. They look pretty interesting. So I shall describe (whatever little I know) in short the ...
0
votes
0answers
19 views

Random selection in percentage

I have $3$ lists of things. I want to choose things randomly from this lists. But have percentage limitation on the lists. Like I can select only $60$% things from $1$st list, $30$% from $2$nd list ...
-1
votes
0answers
13 views

Excel: SUM RAND() outcomes [closed]

I need to do the following: I have event count in column A, like this: 10 1000 5 1 etc. In columnn B, I need to count the number of times RAND() returned less than 0.1 in the number of tries listed ...
0
votes
0answers
15 views

Switching blinding factors securely.

My question is related to information security area and I have asked almost a similar question in: ...
0
votes
0answers
36 views

Euclidean norm of two random variables

I have two normally distributed random variables. $X_1$ and $X_2$ with mean $u_1,u_2$ and variance $s_1^2,s_2^2$. They are independent with each other and have interval $(-\infty,\infty)$. Is it ...
2
votes
1answer
50 views

Measure of card shuffling randomness

I've read online that you need to shuffle a deck of cards at least 7 times (depending on the game being played) for the deck to be 'random enough', i.e. that it is nearly impossible to predict the ...
3
votes
1answer
447 views

Probability distribution of the product of two independent complex gaussian random variables

I have to calculate the pdf of $Z = X*Y$, where $X \in \mathcal{C}(\mu_x,\Sigma_x)$ and $Y \in \mathcal{C}(\mu_y,\Sigma_y)$, where $\mathcal{C}$ is a complex distribution. It can be assumed that ...
0
votes
1answer
26 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 ...
0
votes
0answers
26 views

Is it possible generate all integer number (from 0 to 2147483647 ) randomly without repetition

From a mathematical point of view it's possible do what I wrote in the title? In computer science I could resolve the problem creating an array which contains all value from 0 to 2147483647 and then ...
1
vote
2answers
50 views

Baseball related problem (balls and boxes)

Thanks in advance for any help! So I am trying to figure out if the number of hits an inning of baseball is random, or if hits tend to come in bunches. To do this, I'm just using a fairly small ...
0
votes
1answer
24 views

ideal number gernerator

I was trying to solve a problem on Hackerearth. Here: https://www.hackerearth.com/problem/algorithm/ideal-random-number-generator/ I solved this partially:https://ideone.com/pXkHwQ (passed three ...
0
votes
0answers
20 views

Expected Number of Cycles in Random Permutations with a Random Number of Symbols

It is known that for permutations sampled uniformly from $S_k$ that $\mathbb{E}[C] = H_k = O(\log k)$ (more precisely, $\Theta(\log k)$), where $C$ is the number of cycles in a random permutation. If ...
0
votes
1answer
20 views

How would I go about calculating values for distributed percentages?

This might be really simple, but I just can't see it. I'm working on a game that has 8 items each with a (arbitrary) probability (% chance) of being found: ...
0
votes
0answers
20 views

Random process theory: probability distribution of height vs summits

Imagine I have a matrix of height values ($z$), e.g. a surface height topography. This surface is a random process: randomly rough isotropic surface with Gaussian distribution. What is the difference ...
22
votes
8answers
12k views

What's the difference between stochastic and random?

What's the difference between stochastic and random? I've read in the Portuguese Wikipedia that there's a difference, but I still didn't see this point on English Wikipedia.
0
votes
0answers
31 views

Puesudorandom generation

Hi i have created a stream cipher that creates a'random' stream of numbers(1-99) as subkeys for the message.The generation algorithum is as follows:(key mod (iv+counter)) mod 99.The key is the main ...
5
votes
1answer
854 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
votes
2answers
15 views

Probability of Finding Disconnected Patterns in Digit Positions of Random Integer Sequence

Let's say I have a random sequence of 9 digits. x x x x x x x x x What is the probability of finding '9' in the first position and '93' in the fourth and fifth ...
1
vote
0answers
39 views

The variance of a sum of random vectors

There are $n$ vectors each containing exactly $q$ random variables as elements. Each vector is denoted I$_k$. Each variable within the vector has its own (normal) probability distribution, and the ...
2
votes
1answer
45 views

Expected number of weighings to get heaviest rock

You are given ten rocks and you would like to find the heaviest one. With each weighing you randomly select two of the rocks and determine which of the rocks is heavier. What is the expected number of ...
1
vote
1answer
40 views

Is there a such thing as a quasi-random shuffle?

I've recently experimented with Quasi-random numbers in monte-carlo applications. Is there a way to construct a quasi-random shuffle? By that I mean can I take a sequence $Q$ and shuffle it to produce ...
0
votes
0answers
16 views

Generating random GPS probes

I'd like to generate a certain number of random GPS probes, with the following requirements: The coordinates (latitude and longitude) must be inside a circle with given center and radius. The ...
1
vote
1answer
361 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 ...
3
votes
2answers
61 views

Pseudorandom Number Generator Using Uniform Random Variable

I am working out of Mathematical Statistics and Data Analysis by John Rice and ran into the following interesting problem I'm having trouble figuring out. Ch 2 (#65) How could random ...
0
votes
0answers
14 views

How to calculate the average of $exp(-t^HA(I+B^{-1}A)^{-1}t)$ w.r.t. A and B.

How to calculate the average of $exp(-t^HA(I+B^{-1}A)^{-1}t)$ w.r.t. A and B, where A and B are Wishart matrices and follow $CWis{h_M}\left( {{\sigma ^2_1}{{\bf{I}}_M},N_1} \right)$ and ...
1
vote
2answers
53 views

How to calculate the probability of the next value in a Random Sequence

Assuming that $X$ is the next value in a finite length random sequence, e.g. $$ abbcccaaccbacccabbacababaccccbacabcbacacX $$what would be the $2$-letter most likely to correspond to the value of $X$ ...
2
votes
0answers
38 views

Shuffle Deck $7$ times or$ 8.55$ times$?$

Persi Diaconis showed in $1992$ that in order to shuffle a deck of $52$ cards, you need at least $7$ riffle shuffles. However, in the paper he published, he showed that we needed ...
1
vote
0answers
29 views

Are there any algorithms or formulas to test the randomness of a sequence?

I have a sequence of numbers generated by a programmed computer using pseudorandom functions. Is there a formula which will allow me to see how random this series is? Here is my idea, are there any ...
1
vote
3answers
576 views

Random directions on hemisphere oriented by an arbitrary vector

Hy, i'm writing a raytracer, and for that I need to generate n random vectors that are inside an hemisphere oriented by the surface normal. Ideally, I would also like being able to restrict the rays ...
0
votes
0answers
23 views

Matching probability of uniform character sequences with known bias

A sequence of characters from a $2^a$ alphabet which are uniformly distributed the expected probability of seeing an exact $n$ character sequence from some starting position (no overlap) is $2^{-na}$. ...
-4
votes
2answers
68 views

The Random 666 number. [closed]

Does the number 666 more likely to come up more than other numbers like 777? The register, on stock exchange and at the pump? enter image description here enter image description here
3
votes
2answers
49 views

How to generate random numbers with Laplace distribution using uniform distribution

I want to prove that transfrom $x=\ln\frac{y_1}{y_2}$ generate random numbers with Laplace distribution where $y_1$ and $y_2$ are unifom random numbers $U \sim (0,1)$. And also transform $x=y_1-y_2$ ...
1
vote
0answers
32 views

How can a stopping time be independent of its stochastic process?

I was reading about a special case of Wald's equation, which led me to the following question: If $X_t$ is a sequence of iid RV's, and $\tau$ is a stopping time for this discrete stochastic process, ...
34
votes
3answers
5k views

Why does this not seem to be random?

I was running a procedure to be like one of those games were people try to guess a number between 1 and 100 where there are 100 people guessing.I then averaged how many different guesses there are. ...
2
votes
1answer
53 views

How one can be random when choosing numbers in an interval?

My curiosity came from a lottery game. When you are choosing numbers in an interval you tend to choose some numbers that are relevant to you, when the result of the game is shown you think you ...
1
vote
1answer
1k views

Generate random points on the perimeter of a circle

I have a circle of radius r and access to a random number generator. What is a method to generate random (x,y) values ...
0
votes
1answer
220 views

uniformly distributed random variable

Suppose that a uniformly distributed random variable X can have each of the seven values $-1, 0, 1, 2, 3, 4, 5$ and $Y = X^2-2X$ I want to get the probability mass function of Y I used the ...
0
votes
0answers
26 views

What probability distribution is being sampled from in this code?

I am reviewing a piece of code where random samples are generated using a function genrand_real3 which gives pseudorandom uniformly distributed floating point ...
1
vote
0answers
24 views

How to generate random boundary programmatically?

What should I read to understand how to draw programmatically random oil 'boundary' like on the picture below? Yes, it should go from the top to the bottom and so I don't need these 'long' drops ...