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2
votes
2answers
101 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
35 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
36 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
37 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
40 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
59 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
42 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
21 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 ...
0
votes
0answers
6 views

How do you compare two random number gernators wrt the intended distribution

Let us say we have two random number generators with the same distribution? How do check their closeness to the intended one?
0
votes
0answers
23 views

Probability distribution of location of maximum of random process

I have the following problem: Given a complex function $H(x)$ at positions $x_1, x_2, x_3,..., x_n$ The function values at each position are independent random circularly Gaussian variables, this ...
5
votes
0answers
56 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
24 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
47 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
21 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 ...
1
vote
1answer
2k 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 :)
0
votes
0answers
16 views

Prove that the following function of binary random variables is monotonic

Consider a binary random variable $y$ over the space $\mathcal{Y} = \{+1, -1\}$ such that $\Pr(y = 1) = q$. Consider also $r$ binary random variables $y^1, \ldots, y^1$ over the space $\mathcal{Y}$ ...
2
votes
1answer
80 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
109 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
96 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
29 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
139 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
105 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
47 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
114 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
64 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
179 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
109 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
112 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
93 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
174 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
416 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
139 views

Perfect Random Number [closed]

Is there an algorithm to generate a perfect random number? I know that most random number generating algorithms we see are for generating psuedo-random numbers. Is there any algorithm which generated ...
0
votes
1answer
211 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
260 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
213 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
1k 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
0answers
138 views

How to generate Zipf-like samples, by using scripting language

Is there any scripting language function (like in python or bash) that samples from a zipf-like distribution, for exponent ...
0
votes
1answer
358 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
286 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
689 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
205 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
103 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
427 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?
7
votes
3answers
382 views

Mathematical description of a random sample

Mathematical description of a random sample: which one is it and why? $X_1(\omega), X_2(\omega), ..., X_n(\omega)$, where $X_1, ..., X_n$ are different but i.i.d. random variables. $X(\omega_1), ...
2
votes
2answers
181 views

Probability, Discrete random variables

Let $X$ and $Y$ be independent random variables, taking values in the positive integers and having the same mass function $f(x)=2^{-x}$ for $x=1,2,...$ .Find $P(X\geq kY)$, for a given positive ...
4
votes
1answer
301 views

Questions about generating non-biased random natural number

A. Several years before, I was solving some problems, and one of problems was something like Explain how you can get non-biased random natural numbers between 1~10, with a six-sided(normal) dice. ...
0
votes
1answer
56 views

How to express the traditional variogram for a non 2nd order stationary random function?

Consider an intrinsic RF Z(x) that is not second order stationary. Considering an arbitrary reference RV Z(x0), how to express traditional variogram in terms of covariance of increments expressed ...
5
votes
2answers
225 views

Expected tail and head length of $\rho$ for a finite random function

Let $F: D \rightarrow D$ be a random function on finite domain $D$ of size $n$. It is well-known that, from any $x \in D$, iterating $F$ on $x$ traces out a sequence of values $x, F(x), F(F(x)), ...