# Tagged Questions

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

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### Looking for strictly increasing integer sequences whose gaps between consecutive elements are “pseudorandom”

I am doing some tests with strictly increasing integer sequences whose gaps between consecutive elements show a "pseudorandom" behavior, meaning "pseudorandom" that the gaps do not grow up ...
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### How to calculate the average number of guesses made to guess a number between 0 and 31?

I know this question is very basic, but my question is more about Mathematical thinking. How to think mathematically: Suppose person $A$ chooses a number from numbers between $0$ and $31$, and ...
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### Complexity of a randomly-traveled N*M grid

I made an algorithm that compute a random-path across a N*M grid using backtracking. It start at [N / 2][0] and shall finish at [N / 2][M - 1]. Each iteration he choose a random direction (Left, Right,...
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### Is there a way to mathematically prove my teaching assistant is wrong?

Our design of algorithms class requires all students to enroll in an online $AI$ competition, where each team has to come up with a bot. Before the final lockdown, each team is allowed to challenge ...
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### Mathematicians shocked(?) to find pattern in prime numbers

There is an interesting recent article "Mathematicians shocked to find pattern in "random" prime numbers" in New Scientist. (Don't you love math titles in the popular press? Compare to the source ...
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### Probability: Store opening time

Smith has a small booth where he sells lottery tickets. Customers arrive according to a Poisson process of rate $\lambda$= 1 per minute. He will close the shop on the 1st occasion that $a$ minutes ...
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### Skewness and Kurtosis Excess, maximum allowed deviation for randomly generated numbers

I'm programming a random number generator which generates numbers according to a user-specified probability distribution (Bernoulli, exponential, uniform, pareto, etc). To verify the correctness of ...
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### 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, $N$ ...
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### 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 ...
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### 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. ...
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### 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 &...
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### Switching blinding factors securely.

My question is related to information security area and I have asked almost a similar question in: http://crypto.stackexchange.com/questions/32427/secure-blinding-factor-switching-at-malicious-server-...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 cases)...
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### 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 ...
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### 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 ...
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### 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: ...
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 ...