# Tagged Questions

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

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### Permutations in an Infinite List of Random Numbers

In an infinite list of random numbers from a to b, prove that in this list, there are all possible permutations of n numbers from the list, where n can be any number. Here are some versions of the ...
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### 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 ...
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### scrambled sobol

I need to do a Monte Carlo simulation in high dimension (up to 1000) where using plain Sobol (with Kuo's direction vectors) as a random number generator is not good enough. Therefore I am ...
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### Test to determine whether a huge series of integers is random or there is a pattern?

I have a series of integers in which some integers occur more than others. I want to know if there is a test to determine whether these integers are randomly distributed or some integers occur more ...
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### 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 ...
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### How many random samples needed to pick all elements of set? [duplicate]

If repeatedly picking a random element from a set, what is the expected number of times I'd have to pick before seeing all the elements of the set? Edit: when picking an element, it is simply counted ...
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### Measuring degrees of randomness

Imagine, for simplicity's sake, that we have a set of numbers, each equal to either 0 or 1. Let's call each a bit. Rationally, if the set is completely random, and reasonably large, the probability ...
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### Determine whether a random binary sequence was generated by human or natural process

Given a binary sequence, how can I calculate the quality of the randomness? Following the discovery that Humans cannot consciously generate random numbers sequences, I came across an interesting ...
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### Probability of maximum of a random walk?

Let us consider a random walk denoted by Sn and let Mn be the maximums of the random walk. Now let us consider that this random walk will end at some point k. SO I am stuck how to prove this equality: ...
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### How to punish a riffle shuffle?

It is common knowledge that for a deck to be considered randomly sorted, at least seven riffle shuffles should be used. However, in my experience, very few people will take the time to complete seven ...
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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 ...
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### Probability of the n-th dice matching in 2 groups of sorted random numbers

Say we have 2 groups of 6 6-sided dice. Each group of dice is rolled and then sorted so we have 2 groups of sorted numbers. What is the probability of each die in the group matching the corresponding ...
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### Forced probability using a random number generator, mathematically correct or not?

What might happen if when using a random number generator, if a particular run is not so random, you "help it out" a little bit? For example, if we use a random number generator to simulate $10,000$ ...
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### Is a “deterministic” subset of a random subset random?

Let $S$ be some set and consider $X \subseteq S$ of size $|X|=x$ u.a.r. (among all the subsets having this size). Now, use some properties of this set $X$ to find some subset $Y\subseteq X$ of some (...
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### Arbitrary vs. random subsets: computing probabilities

Let $G=([n],E)$ be a graph having minimum degree $\delta(G) \geq (1-\delta) n$. For some $q=q(n)$, let $G_q=([n], E_q)$ be the random subgraph of $G$ obtained by deleting each edge independently with ...
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### Particle in a box

Say I have a point particle located at the center of a box and imagine that I give it a velocity v in some direction. It will bounce back and forth in different directions maintaining the same speed |...
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### Sequence of non-independent coin tosses

Suppose that a sequence of coin tosses is due to be performed. Let $p_i$ denote the probability that the $i$th coin toss lands on Heads and let $X_i$ denote the corresponding indicator random variable ...
If there are $26$ available capital letters and $6$ available numbers $0$ to $9$ to complete a $6$ "digit" combination (a license plate for example) what is the formula for calculating the number of ...