The tag has no wiki summary.

learn more… | top users | synonyms

0
votes
1answer
20 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
81 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
48 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
votes
0answers
29 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
67 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
0answers
22 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 ...
0
votes
0answers
11 views

The distribution of the random power series

I came across this question below. Let $F(z,w) = \sum_{n=0}^{\infty} X_n(w)Z^n$, where $X_n(w)$ is a random variable, that can be taken either as constant $c_1$ or $c_2$ with same probability of ...
-2
votes
1answer
27 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
38 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
33 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
129 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
83 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
43 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
42 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
62 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
74 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
50 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
vote
0answers
82 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
73 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
55 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
22 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 ...
4
votes
1answer
7k 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
82 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
116 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
169 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
31 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
146 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
134 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
51 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
126 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
69 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
213 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
vote
1answer
145 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, ...
1
vote
2answers
165 views

lottery numbers in parallel universes

i have a question about how randomly generated lottery tickets. recently a woman won the lottery with a random ticket. it turns out that someone let her cut in line ahead of her and this second person ...
1
vote
1answer
155 views

Variance of Matrix Trace

Given a random variables $X \in \mathbb{R}^n$, and a constant real matrix $Z$, how can the variance given by $Var[Tr(ZXX^T)]$ be calculated? Note that $Z$ is p.s.d and $X$ is $N (0,C)$.
4
votes
1answer
185 views

Expected Value of a Randomly decreasing function

We are asked to find the expected value of the following function RDF(N, K) for i = 1 to K do N = random(N) return N ...
10
votes
5answers
581 views

Why do we need “perfectly” random numbers?

I periodically see articles about physicists or others coming up with a technique that generates a slightly more random number than was possible before, and how this is useful for encryption. But ...
0
votes
1answer
241 views

Unexplainable noise graph function.

I'm sorry for the ambiguity here but I've recently discovered a function which plots, what seems to be either a fractal or simply noise in a selected area. Can anyone explain this function: ...
0
votes
2answers
296 views

How to check that a sequence of numbers is random? [duplicate]

I have a sequence of numbers like 1,7,22,45,12,96,21,45,65,36,85,14,51,16,18,17,16....65... IS there any formula to check whether the sequence is random or not ? In my case odd numbers are ...
2
votes
2answers
356 views

Integral of a random function

How is it possible to evaluate the integral: $$I(\mu,\sigma)=\int_0^{2\pi}\sin(\omega t)^2dt$$ where $\omega$ is a random variable having a normal distribution $N(\mu,\sigma)$? What is the $pdf$ of ...
6
votes
3answers
2k views

Why is gradient noise better quality than value noise?

I have been reading about the mathematics behind Perlin noise, a gradient noise function often used in computer graphics, from Ken Perlin's presentation and Matt Zucker's FAQ. I understand that each ...
1
vote
2answers
2k views

autocorrelation of a random process calculation

I know if I want to calculate autocorrelation of a random process , I have this rule : $ R_X (t_1 , t_2) = E \{ X(t_1)X^*(t_2) \} $ . In my cource I had this example : $ X (t ) = A cos(2πft + ...
0
votes
1answer
438 views

Trigonometric function of a random variable

Given the random variable $\nu(t)$ and given the function $$y(t)=sin \left(\pi\nu(t) \right)^2$$ how can I find the distribution of the $y(t)$ knowing that $\nu(t)$ is a gaussian white noise? Thanks
1
vote
1answer
335 views

Determinant of a random matrix

Given the set $A=\{0,1\}$ of all the real numbers between $0$ and $1$, we can build the square random matrix: $$H_2=\begin{bmatrix}h_{11} & h_{12} \\ h_{21} & h_{22}\end{bmatrix}$$ where the ...
0
votes
1answer
891 views

Matlab multivariate normal distribution parameters (mvnrnd)

I need to use the mvnrnd function in matlab to generate random monthly returns for a set of assets. However, I am a bit confused about how to use this function to do it since it asks me MU and SIGMA ...
4
votes
2answers
216 views

What type of distribution would rand()/rand() produce?

If rand() is a function which produces a linearly distributed random number over a range not containing zero, then what type of distribution would rand() / rand() produce? I know it would center at ...
1
vote
1answer
108 views

Random variables and sums of $k$-sided dice

Consider fair $k$-sided dice with the numbers $1$ through $k$ on their faces. a. Roll one die. Let the RV $X$ be the number on one die. Compute $E[X]$ and $V[X]$. b. Roll $n$ dice. Let the RV $Y$ be ...
0
votes
1answer
451 views

Distribution of sum of two random variables

let's say I have two random variables, both have a mean of 0, one has a variance of 2, the other has a variance of 3. How can you determine the distribution of their sum?