How random this numbers look, 21081461046286104621816 Here the system I used to get them, first pick the seed, 13128 then add the value of the 2nd number to the 1st and write it between them and the 3rd to 2nd and write it between them and etc. 143213218 and repeat again 2nd to 1st etc. […]

Are there any random variables so that E[X] and E[Y] exist but E[XY] doesn’t?

Assuming that I have $\{x_1,\ldots, x_N\}$ – an iid (independent identically distributed) sample size $N$ of observations of random variable $\xi$ with unknown mean $m_1$, variance (second central moment) $m_{c_2}$ and second raw moment $m_2$. I try to use sample mean $\overline{x}=\frac{1}{N}\sum_{i=1}^Nx_i$ as an estimator of the true mean. So I want to find its’ […]

I have an assignment for my algorithms module that requires us, amongst other things, to find the equations for the following question. Edit – Question Updated You have n cards with pairwise different integer values from 1 to n , shuffled randomly on a pile. You pick cards from the pile, one after another, and […]

Let’s say I have a regular fair die, but instead of digits 1 through 6, there are three 0s and three 1s. I can generate a random $n$-digit binary number as follows: if initially I roll a zero (or a series of them), I ignore them; then what is left to do is just roll […]

I found a very simple algorithm that draws values from a Poisson distribution from this project. The algorithm’s code in Java is: public final int poisson(double a) { double limit = Math.exp(-a), prod = nextDouble(); int n; for (n = 0; prod >= limit; n++) prod *= nextDouble(); return n; } nextDouble() is a function […]

I recently know that following results. suppose that $x_1, x_2, x_3$ are independent real Gaussian random variables with $\mathcal{N}(0, 1)$. Then $$ \frac{x_1 + x_2 x_3}{\sqrt{1+x_3^2}} \sim \mathcal{N}(0, 1) $$ We can prove this result by direct computing. But I am wondering if there is a simpler way. Also, since this result is interesting. I […]

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 continuously, but they change from a bigger value to a smaller one and vice versa due to the properties of the sequence without an easy way of […]

In school, I was taught to denote a random variable like so: $$R=\{_{0}^{1}$$ This only goes for a random choice between two integers, like a coin flip. How do I write a variable that is equal to a random integer in a certain range, such as, $5$ to $10$?

I am in need of a more generalized solution to this problem. I have a random number generator that generates numbers from 0 to 1. Using this, I want to find $r$ numbers that add to $n$. How do I do this efficiently, and such that the numbers are uniformly distributed? For my specific case, […]

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