The tag has no wiki summary.

learn more… | top users | synonyms

1
vote
1answer
46 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
23 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
53 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
15 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
26 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
30 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
126 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
72 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
42 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
41 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
55 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
71 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
81 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
11 views

How do you compare two random number generators 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?
5
votes
0answers
71 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
26 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
6k 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
115 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
163 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
131 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
68 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
205 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
138 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
153 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
146 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
183 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
556 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
240 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
289 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
345 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
427 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
329 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
873 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
214 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
107 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
447 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?
8
votes
3answers
395 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), ...