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1answer
42 views

zero covariance but not independent - normally distributed random variable $X$ and $X^2$

This is one of my homework question, which the answer sheet has already been given out. However, I still don't understand it. Exercise 1.1. It is well known that for two normal random variables, zero ...
1
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0answers
8 views

fidi of Chi-square Random Field

The $\chi^2$ random field $U(t)$ with $n$ degree of freedom (dof) is defined as: \begin{align} U(t) = \sum_{i=1}^n X_i(t)^2, t\in\mathbb{R}^N \end{align} where $X_1(t),...,X_n(t)$ are i.i.d ...
0
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0answers
24 views

What is exactly meaning of The notion of Sample path and Stochastic Process?

I am wondering what Stochastic Process is exactly meaning. Let me talk about what I understood. I will give an example. $\Omega_i$ is noise of my robot's circuit on July the $i$-th day. The ...
2
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0answers
20 views

More concise $f(x) = (\mathop{\mathrm{rand}}(20)-10)\times 10^{\mathop{\mathrm{rand}}(2x)-x}$?

Assume a typical (I think) PRNG $\mathop{\mathrm{rand}}(n) = \omega$ where $\{\; \omega \in \mathbb{R} \mid 0 < \omega \le n \;\}$ for $n > 0$. I want to create a random function $f(x)$, such ...
1
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0answers
40 views

What's the name of this extremely common but extremely pathological continuous function?

Okay, so let's define a random function $F$, such that the value of $F(x)$ is uniformly distributed on $[-1,1]$, and such that for any $x$ and $y$ with $x \ne y$, $F(x)$ and $F(y)$ are independent. ...
1
vote
0answers
11 views

Auto-correlation of random process (integration)

Consider the following problem: Suppose we know that $f_X(x)=1$, now I want to calculate the autocorrelation: $E[\underbrace{X(t)X(t+\tau)}_{g(t)}]=\int_0^1 g(t)f_X(x)dx=\int_0^1 ...
2
votes
1answer
68 views

Convergence of the fdds vs convergence in distribution in a function space

I'm trying to understand the essential difference between two common types of the convergence of random processes: the weak convergence of the finite-dimensional distributions (fdds) and the ...
1
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1answer
19 views

The rand function/algorithm - when does it begin to develop a pattern?

this question is rather general but I am sure a specific answerer or at-least a theoretical answerer can be provided on it. The rand function is a random number generator that runs on a seemingly ...
2
votes
0answers
13 views

given the power spectral density, how to get $\|\|_{\infty}$ norm

Given the power spectral density of a random signal $P(\omega)$ It is possible to estimate or compute the upper bound of the signal, i.e., the $\|\|_\infty$ norm?
0
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0answers
17 views

Generating random Gaussian fields

I want to generate functions $f: X \to \Bbb R^n$ where $X\subseteq \Bbb [0,1]^m$ is a finite set and $f$ is the restriction of a "nice" (smooth and not too wild) random function $\tilde{f}: ...
1
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0answers
76 views

Invertible pseudo random number generator

I want to create a random sequence using a given seed. However when given a sequence I also want to calculate the seed which produces the sequence. Of course this is not possible using a "true" ...
1
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2answers
34 views

In writing a simulator to simulate an experiment that rolls 2 dice and checks if the sum of the 2 rolls is less than or equal to a given value.

Is it better to use 2 independent random number generators or one array of size 36 that holds the sample space(of all possible sums) and use one random number generator to choose from this arry. ...
0
votes
2answers
41 views

Mathmatical notation of random function

A function $f$ projecting from $\mathbb N$ to $\mathbb N $ is denoted as $f: \mathbb N \rightarrow \mathbb N$. I is OK to denote the common random() function, i.e., without input parameters, as it is ...
0
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0answers
11 views

PRNG Improvements

Purpose This is the (somewhat) mathematical representation of an algorithm for a pseudo random number generator. It uses mostly linear math and generally is not very complex, but then again - I'm not ...
2
votes
4answers
66 views

Random number function (counting)

I have task I can't get my head around, even with a suggested answer. You have a function the generates a random integer between $0 - 65535$. Your task is to generate random integers $125-525$ ...
1
vote
1answer
81 views

Generate random number according to any equation

So I'm after a random number generator where the probabilities of a number occurring in some range is matched to some function. Only really looking at functions with nice integrals (for simplicity ...
0
votes
1answer
32 views

Uniform random number generation

Given a uniform random number generator that generates integers between any given range, a n-tuple $b$, and an integer $c$, how can one uniformly generate n-tuples ($x$) that meet the following ...
4
votes
1answer
88 views

If I assign a random number $r_x \in (0,1)$ to every $x \in (0,1)$ what are the odds that one of them will be a specific number?

I'll start by motivating by question with a simpler scenario to ensure I've at least understood that scenario properly. Scenario 1 : Imagine an infinite sequence of numbers where $i$ is the ...
1
vote
1answer
69 views

Solve for x without using the quadratic formula

Some context: I'm doing an inverse transformation method where I have the probability density function split in three parts. The first part is: $$ f_1:\frac{x-6}{8} $$ For $ 6 < x < 8 $. I ...
0
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0answers
46 views

explanation : Example of Gaussian random process?

Can any one explain to me how to answer the question and what is the Gaussian random process in a simple way. I know how we find the C xx from R xx the rest of the answer I don't understand why all ...
1
vote
2answers
154 views

What are some fast ways to generate random numbers?

Many programming languages come with a function to give random numbers. I wonder how they implement that. Also, assuming the language doesn't have a random function, is there a way to generate them ...
0
votes
1answer
41 views

Generate list of random items without dublicates

I need to generate list of random int items without duplicates. for example: n = 6( 0, 5, 2, 3, 1, 4). I write simple algorithm based on ...
-2
votes
1answer
28 views

is it possible to implement random(0,1,..,m) with finite calls to random(0,1)? [closed]

that is, is there a function $f$ that $Y=f(m,X_1,X_2,...,X_{n(m)})$ where $X_i\sim B(1,\frac{1}{2})$ and $Y\sim U\{0,m\}$? e.g. when $m=2^k-1$,$n(m)=k$ and ...
-1
votes
1answer
47 views

How to find the distribution of a function of multiple, not necessarily independent, random variables? [closed]

If $Y$ is a random variable defined as $Y=g(X_1,X_2)$, where $X_1$ and $X_2$ are two different random variables whose distributions are known (say with pdf's $f_{X_1}$ and $f_{X_2}$), how do we find ...
1
vote
1answer
44 views

The autocorrelation function of i.i.d process

$\{x(n)\}$ is i.i.d; therefore, it is strictly stationary. Can I say the autocorrelation function $\{x(n)\}$ is a delta function, that is $R_X[k] = N_0\delta(k)$? Thanks
2
votes
2answers
144 views

Would Evaluating a polynomial at uniformly random points outputs random values?

I`m wondering if we evaluate a polynomial on many points picked uniformly at random. Can we say the output values Y's are uniformly at random?
-1
votes
1answer
180 views

finding out the probability density of a random process

I have to find out the probability density function of a random process with the following specifications:z(t)= xcos(wt)-ysin(wt) where x and y are two independent gaussian random variables. Now what ...
1
vote
1answer
45 views

Is a function with a random variable continuous?

I often like to fool around on graphing calculators when I am bored. A function that can be very amusing is $f(x) = rand \times \sin x$ Now, on my TI-84 Plus, this looks obviously discontinuous ...
0
votes
1answer
45 views

differential equation with random coefficient

I am confused with a problem I encountered at hand, not on how to work on it but rather understanding the problem itself: Let $A(x;\omega)$ be a random field taking values in $[a,b]$ where $a,b < ...
0
votes
4answers
72 views

Generate random numbers in a random fashion

How can I generate 9 random numbers between 1 to 9,without repetition, one after another. Its like: Lets assume that the first random number generated is 4, then the next random number has to be in ...
1
vote
1answer
89 views

finding the limits of integration for joint probability

I have three variables $x_1$, $x_2$ and $x_3$. Their joint dist. is $f(x_1,x_2,x_3)= \exp(-x_1-x_3)$, where limits of $x_3 = 0$ to $\infty$, $x_2 = x_3$ to $\infty$ and $x_1 = x_2-x_3$ to $\infty$. ...
1
vote
0answers
57 views

Why does a Gaussian process have a gradient whose determinant is Gaussian?

I'm trying to understand something in Adler and Taylor's book, Random Fields and Geometry. Let $T \subset \mathbb{R}^N$ be a compact parameter set (for simplicity, suppose it is a closed hypercube) ...
1
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0answers
89 views

Ideal shrinking of discrete randomness source

I have a discrete randomness source that emits random integer numbers in range [0..N) with uniform distribution. I need to reduce this distribution, limiting it to ...
5
votes
0answers
81 views

Decrease of entropy when iterating a random discrete function

Let $m$ be a positive integer. Let $S$ be the set of non-negative integers $x$ less than $m$, with $|S|=m$. Let $X_0$ be the discrete uniform distribution over $S$, with $P(x)=\begin{cases} 1/m & ...
1
vote
0answers
27 views

The “size” of a continuous uniform selection of points in the unit square

Let $\{X_r\}_{r\in[0,1]}$ be i.i.d. random variables, each distributed uniformly on $[0,1]$. Let $S\subseteq[0,1]^2$ be the random set defined as follows: $$S=\{(r,X_r)\mid r\in[0,1]\}$$ How would ...
1
vote
2answers
64 views

Product & Ratio's of 2 Random Variables

I'm interested to know whether it's the case that for random variables $X$ and $Y$ whether or not the ratio of $X$ and $Y$ can be computed as the product of $X$ and $1/Y$. That is, Is $\frac{X}{Y} ...
0
votes
1answer
25 views

Looking for a random statistical biaised function

A common random function is designed like a dice, if you call it many times it will yield approximately the same number of times 1, 2, 3, 4, 5 and 6. Statistically, you could say it's equally spread ...
6
votes
1answer
13k views

'normally distributed random numbers' vs 'uniformly distributed random number'?

what is the difference between 'normally distributed random numbers' and 'uniformly distributed random number'? A answer in a layman language is appreciated :)
2
votes
1answer
89 views

How does a random function $f:\{1,\dotsc,N\}\rightarrow\{1,\dotsc,N\}$ look like?

For every $n$, write $[n]=\{1,\dotsc,n\}$. Let $\{f_n\}_{n=1}^\infty$ be a sequence of random functions $f_n:[n]\rightarrow[n]$. By "random functions", I mean that the value of each $f_n(i)$ is chosen ...
0
votes
2answers
119 views

How do you generate a surface who's value around the origin is within some range

What's a quick way to generate a smooth, closed-form surface that will be within the range $[0,1]$ for $x, y \in [-1,1]\times[-1,1]$? The surfaces should be of similar complexity to $2\times2$-degree ...
0
votes
1answer
218 views

Frequency analysis/discrete uniform distribution in multiple choice tests

I may be using the wrong terms in the title but I read that if something is random then each character will occur an equal amounts of times. I read this when reading about the One-Time Pad cipher, ...
2
votes
1answer
32 views

Convergence of a series of random elements

Given the normally distribuited random variable $\nu(t)$ with $\mu=0$ and variance $\sigma$, I have to find if the series: $$G(\sigma)=\sum_{k=1}^{\infty}\frac{1}{\exp\left(\nu(k)\right)}$$ where ...
2
votes
0answers
147 views

Finding functions where the increase over a random interval is Poisson distributed

I'm trying to construct a type of function $f(t_1, t_2)$ that counts the number of deterministically simulated Poisson events between two points in time. We can use a single valued function ...
2
votes
1answer
158 views

Random processes: Repair time

I have a question that is to do with qeueing theory and repair times: Assume that a small office has 4 printers. Each printer breaks down independently of the other printers and independently of the ...
0
votes
1answer
52 views

Conditional probability over a function

I have a question if the following relations on conditional probabilities hold for independent random variables? $$P_{X \mid Y, G(Y)}(x_1)=P_{X \mid \{Y\}}(x_2)$$ where $G$ is not necessarily ...
0
votes
1answer
133 views

Conditional distribution of a function of random variables

I have a question about conditional distribution. Suppose we have three independent random variables $X_1$, $X_2$, $X_3$. Then we have mapping $Y_1=g(X_1, X_2)$. The mapping is not necessarily an ...
0
votes
1answer
81 views

Sum of poisson random variables on a lattice

Consider a lattice $\mathbb{Z_+}$ and immagine that on each site $i \in \mathbb{Z}_+$ there is a number of particles $X_i$, where $X_i$ are i.i.d. Poisson random variables having expectation $\mu$. ...
5
votes
1answer
254 views

Generate random numbers between a range such that no number comes twice.

Sorry if my question is stupid, math has been always a wild beast for me. I am an application developer. In one application I have a module which assigns a random 6-8 digit number and a serial number ...
1
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1answer
186 views

Expected minimum distance of a random point with respect a set of random points on the plane

I need to estimate, or bound, the expected minimum distance of a random point with respect to a set of other random points, all of which are located inside of a bounded rectangle. More specifically, ...