Questions tagged [random-functions]
This tag is for questions relating to the functions of random variables which is a function from $Ω$ into a suitable space of functions (where $Ω$ is the sample space of a probability space that has been specified). Technically, there is also a measurability condition on this function.
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Prof. Knuth lecture about $ \pi $ and random maps
In this video, Prof. Knuth talks about an interesting combinatorial problem:
suppose you have a random map $ f\colon \{ 1, 2, 3,\ldots, n \} \rightarrow \{ 1, 2, 3,\ldots, n \}$. If you consider the ...
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What kind of functional space can be used to describe power signal? [closed]
Most signal in Engineering is power signal, of which the power is limited while the energy is infinite. For example, the noise in a transceiver has limited variance and exists as long as power on. ...
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On the Existence of Continuous Versions of Stochastic Processes
Let $g(t, x)$ be a continuous function on an open set $S \subseteq [0,T] \times \mathbb{R}^d$.
Let $X_t(x)$ be an $\mathbb R^d$ valued random field where $t \in [0,T]$ and $x \in \mathbb{R}^d$ which ...
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a basic question on random process
I am currently studying the infimum of a random process, however, it seems we can study it according to its supremum, but I am not sure my naive thought was correct or not. Speficially,
consider ...
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Distribution of difference of two random variables
The problem is following:
Suppose we have a line segment with a length $L$ and we randomly choose (with uniform distribution) $n$ points on this segment, so we divide the main line segment into $n+1$ ...
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Function of exponential random variables
I have $20$ exponential random variables with mean $\alpha$ representing delays $D_n: n \in\{1,\ldots, 20\}$.
I have 20 random variables denoting power $P_n^{'}: n \in\{1,\ldots, 20\}$. which depends ...
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What is the limit probability an element of $x \in S$ belongs to $f^n(S)$, for $n \to \infty$?
Let $S$ be a finite set of $|S|=n$ elements and $F$ be the set of all functions $f:S\rightarrow S$.
It's easy to demonstrate that the integer sequence $\{c_i\} = |{\rm Im}(f^i)|$:
is non increasing;
...
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1
answer
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Randomly Generating Real-Rooted Polynomial Equations
I need a simple function to generate real-rooted polynomial functions to demo my Desmos Aberth-Ehrlich rootfinding implementation.
My current function is as follows:
Let $n \in \mathbb{Z}^+$ be the ...
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Random functions and neuronal network
Let f be a continuous function on $\mathbb{R}$ and B_t a brownian motion.
Is there any density result of the neuronal network class for function of the form $t \mapsto f(B_t)$ ?
user1040055
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Birthday problem: how to show the scaling with $1/N^2$?
Suppose there is a sequence of$N$ numbers $x_1, x_2, x_3, ... x_N$.
There are then gaps $|x_i - x_j|$, and the minimum gap:
$\delta (N) = \text{min}_{i \ne j \le N} \{ | x_i -x_j | \}$.
Let the mean ...
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Keener Lemma 9.1 proof
I'm reading the book Theoretical Statistics by Keener, and I couldn't figure out one of the claims in the proof for Lemma 9.1.
Lemma 9.1 states: let $W$ be a random function in $C(K)$ where $K \subset ...
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How to prove that a set of mathematical operations is actually a pseudo-random permutation?
The area of PRNG is mostly an experimental area. I have created a simple PRNG (called komirand) which passes statistical tests for randomness in ...
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How does an integral change the distribution of a random variable?
Suppose I have a random variable $x$, and I want to perform the integral of a function of $x$ such that:
$$y=f(x)=\int_{c_l}^{c_u} f(x,c) dc$$
where $f(x,c)$ is a nonlinear function of $x$ and $c$. ...
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Does distribution of input with a given entropy matters to the entropy at the output of a random function?
For random functions with $k$ input and output values, we can define the expected Shannon entropy of the output when the input has a uniform distribution (with the expectancy over all random functions)...
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Convergence of expectations of bivariate functions
Suppose I have a continuous bivariate function $g:\mathbb{R}^2\rightarrow [0,\infty)$ that is increasing in both arguments and uniformly bounded by some constant.
I also have three sequences of random ...
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