# Tagged Questions

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

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### 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 ...
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### Unranking pseudo-random values to produce uniform distribution over all permutations

Following this question (and answers) on SO. The problem is to find a method to produce an unranking of combinatorial objects in random order, but in such a way that all possible orderings are ...
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### Series of random numbers on a continuous function

At one point, I read about a function used to generate random numbers that follow a continuous pattern. By this I mean random numbers that as a series is random, but in which items tend to be ...
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### Random numbers within a range?

(Note: When I say "random" just assume I mean pseudo-random) I have heard that random numbers are generated using this method: $X_{n+1} = (a X_n + b)\, \textrm{mod}\, m$ Using the time as the seed. ...
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### Creating random numbers matching mean and standard deviation

I know how to compute mean and standard deviation for a given probe. But how do I the opposite? Given is the wanted mean and standard deviation and I want to create the probes. In other words: What ...
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### 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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### 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 ...
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### Calucluating probability of randomness of number in given range

Ok. Here's a question I just read in a book relating to combinatorics and probability. I'm not able to make head and tail about how I should approach it, so here goes: You have a device that ...
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### Distribution of a random measure is determined by the characteristic function

I ham trying to understand a proof from a book I am reading. It says the proof follows directly from the prior theorem and I just can't see that. Let $X$ be a random measure on a locally finite, ...
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### Function (algorithm) for obtaining random number(s) from dice

I'm afraid I don't speak maths very well. I hope this question is sufficiently comprehensible and mathematical. Suppose I have a perfect D$x$ (i.e. $x$-sided) die, and a pen and paper, and with these ...
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### Monte Carlo gamma function

This question was asked before but I'd like to ask something more precise given the answer that was given. [ Estimate gamma function using monte carlo ] What is the criterion for a random point to ...
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### Can you generate math problems that are solveable?

If you take Linear Programming, it problems are formulated like this: You know that Cabinet X costs 10 cents per unit, requires 6 square feet of floor space, and holds 8 cubic feet of files. ...
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### Covariance of a random variable and its mean estimator

I was wondering if there is a common solution for the covariance of a random variable $x[n]$ (i.i.d) and its mean estimator $\hat{\theta}$. Mathematically, \sigma^2 \left ( ...
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### Solution for the Tall movie-watchers problem!

The question which I write is a changed format of what I have faced, in my project. I changed it to an attractive question and named it by "tall movie-watchers problem": Suppose that a small cinema ...
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### Magnitudes of roots of random polynomials

I'm looking at the roots of random polynomials with integer coefficients, and constant term=leading term = 1. Using the Mathematica code ...
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### Dividing gems by random permutation

A group of people have found a treasure of gems: $G=90$ green and $B=990000$ blue. They decided to divide it among them. Since there are more people then gems, they decide to order themselves in a ...
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### Unexpected behavior with random numbers

I am trying to write a program dealing with random number generation, but I figured this would be the best forum to ask this. My program will, given each of the March Madness teams' probabilities of ...
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### Random Shots and percentages behind it.

Just to be clear I am rather bad at math, however I am making a webservice and need to understand the math behind it in order to recreate it in javascript. So here goes.I am trying calculate the ...
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### Covariance and correlation of summations of independent random variables

This is the problem: There are 2n β 1 independent random variables X1, π2, ... , π2πβ1. The expectation E(Xi) is ΞΌ for all i = 1,...,2nβ1. The variance Var(Xi) is Ο2 for all i = 1,...,2nβ1. Let ...
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### Question about noise term in SDEs

Do any properties/assumptions of SDEs prevent the noise term from being extremely large? Using a simple population growth model as an example, $\frac{dNt}{dt} = (r_{t} + W_{t})Nt , N0$ given, ...
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### Does randomness exist? [closed]

I've been plagued with this question for a few years now and wanted to know what others think. Does true randomness really exist? In mathematics, a random process is based on the concept of random ...
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### Generate list of random items without dublicates

I need to generate list of random int items without duplicates. for example: n = 6( 0, 5, 2, 3, 1, 4). I write simple algorithm based on ...
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### spectral norm of a sparse Gaussian matrix

Suppose $G$ is an $m \times n$ matrix such that each entry of $G$ is a standard normal variable. We know that the spectral norm of $G$ scales as $\sqrt(m) + \sqrt(n)$. Now, given a set of indices $S$ ...
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### Given a list of integers between $0$ and $99$, create a function that will fit all the integers in the list.

Okay, so my friend LOVES to play the lottery. He makes bets often with bookies on the last $2$ digits, getting $90:1$ on his money, a losing bet. He looks up 'systems' on social media on how to ...
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### Multiple rolls of a one hundreded sided dice

Let's side I have a one hundred sided dice and a friend picks 8 random numbers from the dice. I understand that if I roll the dice one time, he has an 8% chance of getting the roll correct. My ...
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### is it possible to implement random(0,1,..,m) with finite calls to random(0,1)? [closed]

that is, is there a function $f$ that $Y=f(m,X_1,X_2,...,X_{n(m)})$ where $X_i\sim B(1,\frac{1}{2})$ and $Y\sim U\{0,m\}$? e.g. when $m=2^k-1$,$n(m)=k$ and ...
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### Random allocation of groups of objects to agents

I have a poorly specified random allocation problem, which I need help in trying to tighten the definition and consider an effective algorithm. I have groups of objects, each group containing at ...
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### Probability that an individual cheated and knows a random sequence.

Bob writes down a sequence of coin flips on a piece of paper and hides it away. He uses a coin flip to determine if he uses a 1 or a 0. Alice tries to guess the random sequence and may have looked at ...
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### What's duplication probability of the next discrete random number?

If I already have n random numbers(between 0-100), what's the duplication probability when I random next number? This is a chart represent probability(0-100%) of this question when n is between ...
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### What would be the maximum number of guesses for a random number between 1 and 9?

How many guesses could someone get wrong if they were trying to guess a number between 1 and 9, with the integer always changing with each attempt? For example: If a random number generator had ...
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### What is a thorough method to manually generate a random number between 1 and 100?

The other day, I got an idea. I would like to generate a random number between 1 and 100 , however by hand. And only using simple tools like a desk clock and pen and paper. What might be a way to do ...