The random-functions tag has no wiki summary.
2
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1answer
74 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
37 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
53 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
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1answer
35 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
63 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 ...
0
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2answers
93 views
1
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1answer
49 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
61 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
43 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
154 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
242 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 ...
1
vote
1answer
104 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
100 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
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2answers
190 views
How to check that a sequence of numbers is random?
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
126 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 ...
5
votes
3answers
594 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
742 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
60 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
139 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
171 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
2answers
411 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
197 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
88 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
348 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
358 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
148 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
213 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
46 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
204 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)), ...
