# Questions tagged [random]

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

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### Calculate the seed of a PRNG from a list of random numbers

Lets say i have a list of randomly generated numbers. Example: import random i=1 mn = 1 mx = 2 while i<500: print(random.randint(mn,mx)) i=i+1 Only ...
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### Period of a Linear congruential generator

I found by experimentation that for the pseudorandom generator described below, the period is 32 (https://repl.it/repls/EasySphericalPhysics). $X_0=0$ $X_{n+1}=(34 * X_n + 17) \bmod 97$ Although ...
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### mean square continuous and diferentiable

Random Process $\{X(t) = min(t,\tau), t \geq 0\}$, where $\tau$ is an $Exp(\lambda)$-distibutet random variable. Prove that X is mean square continuous and mean square differentiable. So for mean ...
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### How to get probability of getting only those items from box which you did not pick before?

I have a box which contains $n$ unused items (all items in the box are unused). From them I randomly pick $k$, where $k < n$ items. Those $k$ items became used when I picked them, and then I put ...
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### How does the Random Number Generator work?

I've always wondered that if computers or calculators for that matter work exactly the way we program them, then how is it possible for them to generate random numbers that are unbiased. How do they ...
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### How can the Johnson-Lindenstrauss Lemma be true, intuitively?

I have read this article about Johnson-Lindenstrauss Lemma can preserve distance-related property from reduced high-dimension matrix only by multiply it with random matrix with standard normal ...
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### looking for functions that are randomized, aperiodic, non-recursive, … (help my terminology)

Context I'm creating a video game with a generated world that can be very large in scale (beyond what will fit on the machine). I want to have some very large objects, where the user might only be ...
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### What does “Random Rotation Matrix” really mean? How to generate it?

I got the term from this paper and I don't understand what it means. It said the "Random Rotation Matrix" can be generated following "Haar Distribution". I only know the output is a matrix which ...
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### Why generating Pseudo-random Numbers by Linear Congruential Generator, the X will follow a uniform distribution?

To be specific, attached is the algorithm of LCG: My question is why X follows a uniform distribution while generating X in this way? And why we use this way to generate X which follows uniform ...
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### Is it possible to change the order of random samples such that no statistical test can detect the change?

Consider I have a 1 million fair die tosses which is will be used in a true random number generator. Can an adversary change the order (just swap a pair of numbers or two) in the sequence such that ...
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### Naming continuous-time random walks

Is there a standard notation for naming continuous-time random walks according to their probability distributions? For example, Lévy flights as Cauchy-based random walk, Rayleigh walk as Gaussian-...
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### How to mathematically represent pore distribution?

I'm currently working on mechanical modeling of microstructural samples and I have a question. Can anyone tell me is there a way to mathematically express distribution of pores in a certain area. I ...
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### random natural number from range using negative binomial

How can you extract a random number from a range using the negative binomial distribution? For example: the range of possible result values is [1,10] the probability of success is 0.2 I really don'...
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### Impossibility of deriving the Born Rule?

Background Let's say I have a physical system. When a measurement happens we apply the Born rule to say which outcome is likely. Now, while a lot of physicists are of the opinion the measurement is ...
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### Random walk on $x$-axis - Probabilities

Exercise : A particle is moving randomly on the $x$-axis. At each instance of time, it moves either right with probability of $p$ or left with probability $1-p$. Each step of movement is ...
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### expected hitting time of asymmetric random walk

$X_1$, $X_2$, ... are i.i.d. random variables with distribution P($X_i$ = 1) = $\frac{2}{3}$, P($X_i$ = -1) = $\frac{1}{3}$. Let $$S_n = \sum_{i=1}^n X_i$$ For each integer k > 0, define T_k = min \...
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### question about Random probability measures

Let $(\Omega,\mathcal{F},P)$ be a probability space and $X$ be a Polish space. Let $\mu:\Omega\rightarrow Pr(X)$ be a random probability measure with marginal $P$ on $\Omega$ and $\mu_\omega$ be the ...
$X$ is a random variable with known pdf. I do have the expectation of a function of X. $\mathbb{E}[f(X)] = A$. Is f unique? I also have multiple sets of vector $(x_1, ..., x_n)_t$ known, where $t$ ...