# Questions tagged [random]

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

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### Prove or disprove: There is a way to choose independent random chords in a circle so that their intersections are uniformly distributed in the circle.

Prove or disprove: There is a way to choose independent random chords in a circle so that their intersection points (given that they exist) are uniformly distributed in the circle. One common way to ...
1 vote
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### Distribution of distance between eigenvalues for GOE when $n=2$

This question is a possible duplicate of PDF of the Difference of Eigenvalues of a GOE I was reading Introduction to Random Matrices Theory and Practice by Giacomo Livan, Marcel Novaes, Pierpaolo ...
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### Weak convergence of a random stochastic process [closed]

I would like to know if I well understood the notion of "weak convergence of a random stochastic process in $(C([0,\infty[), \left| \right|_{\infty}$. Is it true that : Given a sequence of ...
1 vote
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### Covariance of functions of two random variables

I am trying to show the following: Suppose that x and y follow identical and independent distribution. F(x, y) is an increasing function of x and y. Is there any way to show that the covariance ...
39 views

### Probability of a pair in "strip" card shuffle. [duplicate]

I was playing around with a deck of cards and I wanted to try out what the odds for a identic pair of cards during a strip-like shuffle were. What I mean by strip like shuffle is the shuffle of the ...
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### Definition of the convergence in probability of a random measure

I'm kind of confused about the definition of convergence in probability of a random measure $\mu_{n}$ to a deterministic limiting measure $\mu$, which are probability measures on $\mathbb R$. Question:...
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### Randomize/shuffle sound tracks to play each one for a preset portion

Suppose you have $n$ sound tracks, $n_1, n_2, \ldots, n_n$. Each has a duration of $x_i$ minutes, so track $n_1$ is $x_1$ minutes, $n_2$ is $x_2$ minutes,... etc. You pick one track by a randomizing ...
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### Expected number of attempts to generate random binary sequence of length N containing at least x 1's

I'm generating random binary sequences of fixed length N Example with N=10: 0101011100, this one has x=5 1's How often do I have to generate such a sequence until I get one with at least x 1's on ...
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### Estimate the average difference from the expected amount of bit-runs in true random data?

I'm creating blocks of totally random bits using a TRNG and per X amount of bits I count the number of times "bit-runs" of different lengths occurred. With bit-run I mean sequences of ...
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### Why does the distribution of entropy in a deck of shuffled cards not follow a normal distribution?

Around a year ago I did a study on shuffling cards and came across an unexpected result. I was investigating methods for quantifying how "shuffled" a deck of cards was, such as measuring the ...
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### Algorithm implementing multivariate normal distribution from Sobol QRNG

My goal is to implement a mathematically correct multivariate normal distribution using Sobol QRNG sequence as a source of randomness. The implementation should NOT produce the whole set of a given ...
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### Probability of Random Integers in a series of ascending/descending Runs

Suppose you have a set of $N$ random integers. Each integer is limited to the range from $0$ to $99$. You then consider each subsequent neighbor as "ascending" or "descending", ...
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### Threshold for the "number of UUIDs generated per millisecond" at which the collision probability of UUID v4 and UUID v7 is equal

I post this question here instead of StackOverflow because the mathematical element is stronger than engineering one. First, let me clarify the definition of terms. UUID v4: Random value of $122$ ...
1 vote
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### Randomness of rightmost bits from LCGs

Task: Show that the sequence of integers made up of the $k$ rightmost bits generated by an LCG with $m = 2^n$ has a period of at most $2^k$. I actually get a hint to define the output as the following:...
Suppose I want to randomly sample (x,y) from a bivariate gaussian/normal distribution: f(x,y) = \frac{1}{2\pi\sigma_x\sigma_y} \exp\left(-\frac12\left(\frac{x^2}{\sigma_x^2} + \frac{y^2}{\sigma_y^2}\...
If we have $n$ coin tosses and we want to prove that the coin will eventually land heads, will this proof be considered a proof of a.s convergence? Let's consider a contracting sequence of events \$A_1,...