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

# Questions tagged [random]

1726 questions

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### Determine the maximum period of this potential random number generator, if possible

Determine the maximum period of the following potential random number
generator, if possible.
$x_{n+1} = 65x_n+1 \,\,(\text{ mod } 2048)$
This is an exctract of a big task with more RNG's and I choose this one to see if I do it correct?
I read…

eyesima

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### Can I generate a random number with the probability distribution of the area under any arbitrary function?

If I want to generate a random number from 0 to 1, for example, if I wanted a uniform distribution, I would give the function $y=1$. If I want a simulated normal bell distribution, I could try something like…

Maurdekye

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### Is product of random numbers still random?

If I have a function f that generates a random number uniformly distributed between 1 and 5 then can I say that g=f*f generates a random number uniformly distributed between 1 and 25?

JohnyC

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### Generating random versions of cubic and quadratic curve

this might be a basic question to you guys but me having very limited(near to none) applied math experience I am not sure to figure this out rightly.
I've two kind of curves cubic and quadratic and I need a function to randomize them. say for e.g…

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### Prove that central limit theorem Is applicable to a new sequence

Let $\xi_1, \xi_2...$ be i.i.d. random variables. $\mathbb{E}\xi_i = 0, \mathbb{E}\xi^2_i = 1 \ \forall i $. Let $\lambda_1, \lambda_2, ...$ be a sequence of real number such that
$$
\frac{\max_{k \in \{1, ..., n\}} \lambda_k^2}{\sum\limits_{i=1}^n…

Elnur

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### Decide if $y(u,t)$ a zero-mean random process.

A communication signal $x(u,t)$ is transmitted to a receiver, which, because of two distinct paths of transmission, observes the received signal $y(u,t)$: $y(u,t) = x(u,t) + c x(u,t-t_m), t \in (-\infty, \infty)$, where $c$ and $t_m$ have known…

Wei-Cheng Liu

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### Decide if $X(t)$ is a Gaussian random process.

Let $X(t)$ be a wide-sense stationary (WSS) random process with the autocorrelation function $R_{XX} = \sigma^2 e^{-\alpha \tau^2}$. Is $X(t)$ a Gaussian random process?
Here is my try:
A random process $Y(t)$ is a Gaussian random process if the…

Wei-Cheng Liu

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### Equation with expectations and squares

Can somebody tell me, why the following is true:
\begin{equation}
\sum_{\alpha,\varepsilon} (f_{r}(\alpha,\varepsilon)-E[f_{r}])^{2}
=\sum_{\alpha,\varepsilon} f_{r}^2(\alpha,\varepsilon)-\sum_{\alpha,\varepsilon}E[f_{r}]^{2},
\end{equation}
where…

koala

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### Random points in sphere following density curve

I want to generate a series of points in a sphere following a density curve (x is distance to sphere center, y is quantity of point at this distance) and I have no idea where to begin with.
Thanks in advance !

Titouan D.

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### An equation about random variables

Consider two mutually independent random variables ${v_1},{v_2}$, which are the Gaussian white noise with distribution $N(0,1)$. We suppose they satisfy the following equation $({v_1}+a_1){w_1} + ({v_2}+a_2){w_2} = 0$, where ${a_1},{a_2}$ are the…

wenbo

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### Sequence of vector of random variables

I'm struggling a lot with below problem:
Let's take a sequence of independent two-dimmensional vectors of random variables $(A_n, B_n)_{n=1}^{\infty}$, where all vectors are uniformly distributed on square $[-2,2] \times [-2,2]$. Let $V_n=(S_n, T_n)…

pocraka

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### tetrahedrons, points, and spheres

this problem is a tricky one that i can't really sum up as a title, but this is the basic jist: a few days ago, my friend gave me this geometry problem:
Given four random points on the surface of a sphere, what is the probability that the…

Alexander Day

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### Xor probability one time pad decrypt

I've got a probability problem that outstrips my knowledge so I'd be grateful for any help. I've looked online for an answer and also on maths sites but it didn't help. The answer would also help others in the same situation. The issue is :-
I am…

Bipman

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### Find the joint density of sum process $f_{S_k, S_{k+1}}(s_k, s_{k+1})$

Given two sum process:
$S_k = X_1 + \ldots + X_k$
$S_{k +1} = X_1 + \ldots + X_{k+1}$
where all $X_i$ are iid random variables
I am required to find $f_{S_k, S_{k+1}}(s_k, s_{k+1})$ e.g. their joint PDF
Attempt:
We know that through independent…

Fraïssé

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### Random Variable Distribution Example Problem

I have difficulty on answering this question, I have done a few research but it doesn't help me to do this question. This is probability question, and I don't know what kind of formula should I use to answer this question.
If 2/3 of the…