Questions tagged [random-variables]
Questions about maps from a probability space to a measure space which are measurable.
12,347
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Optimizing a Dynamic Fitness Function with Differential Evolution Across Multiple Time Steps
I have a dynamic fitness function f(x,t) that I need to optimize using Differential Evolution (DE). Here, t represents time ...
- 135
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2
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51
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Commutative diagram involving order statistics
Given the random variables i.i.d. $X_1, \ldots, X_n$ and their cdf $F$ I'm trying to explain why the following diagram is conmutative:
$$
X_1, \ldots, X_n \xrightarrow{\text{sort}} X_{(1)}, \ldots, X_{...
- 115
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Known correlations [closed]
A bit lost on where to get started on this problem — any thoughts would be greatly appreciated!
I know X + Y is normally distributed with N(0, 2), not sure how to compare two normally distributed ...
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33
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Distribution of $T_j$
I have a binary matrix (All elements are $0$ or $1$) $A \in \mathcal{R}^{K\times L} $ with some rules.
The rules are as follows:
Each row must have $R$ $1$s.
Each column must have $C$ $1$s. $(C = \...
- 11
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Why are limits of $L^p$ sequences defined almost surely? [closed]
I have heard it said that if a sequence of random variables $\{X_n\}$ converges in $ L^p $, then it converges to a limit $ X $ that is defined almost surely. I am trying to understand the precise ...
- 135
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2
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Chf. of a sum of independent r.v. is the product of chfs. Is the converse true?
Let suppose that we have a random variables $X$ and $Y$ whose chfs. can be written as:
$$\forall u \in\mathbb{R},\quad\Phi_X(u) = f(u)\Phi_Y(u).$$
Does it mean that we can write $X=Z+Y$ where $Z$ is a ...
- 506
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1
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38
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Generating function of $P_{11}^{2n}$
I am studying Markov chains and I am interested in calculating the generating function ($U(s)$) of $P_{11}^{2n}$, where
$$
P = \begin{pmatrix}
0 & 1-\alpha & \alpha & 0 \\
...
- 753
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What are the "standard" topology for a space of random variables?
Suppose $\mathbb X$ is the space of random variable over $(S,\Sigma, \mu)$ with finite support. What are some commonly used topology for $\mathbb X$?
Reason of asking: I am reading a paper which uses ...
- 830
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How can I calculate the rate of overlapping events between two Poisson processes?
I have the following problem: I have 2 independent Poisson processes with a known rates λ1 and λ2.
The events in each process have a well-defined duration, D1 and D2.
From that, I need to know: What ...
- 131
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Distribution of a product of random variables
I have two independent distributions $X$ and $Y$. $X$ is defined by the piecewise CDF
$$F_X(x) = \begin{cases}
F_X^1(x) & x \in (-\infty, a_1)\\
F_X^2(x) & x \in [a_1, a_2)\\
F_X^3(x) & x \...
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What is the formula for PMF from adding independent zero-modified negative binomial random variables?
Let $X$,$Y$,and $Z$ be independent identical zero-modified negative binomial (ZMNB) random variables, then how would the probability mass function (PMF) be calculated?
$$P(X + Y + Z = k) = ?$$
For ...
- 11
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1
answer
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Weak convergence of degenerated random variable with finite support. Does it work?
This is what I learnt:
The requirement that only the continuity points of F should be considered is essential. For example, if Xn are distributed uniformly on intervals (0,
1
/
n
), then this ...
- 830
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Independence of Random Variables $Z_1=\min\{N_1,p\}$ and $Z_2=\min\{N_2,p\}$.
Suppose that $N$ particles (a fixed quantity) are randomly distributed in the interval $[0,1]$ and the particles are independently coming from the uniform distribution in $[0,1]$. Now consider any two ...
- 33
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Probability winning game where you order random variables as you go along
Let us pick $n$ independent random variables from $U[0,1]$, one at a time. After you see what $X_1$ is, you have to guess what position it will come in out of $n$. Then you see what $X_2$ is and have ...
- 5,633
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Standard deviation of the norm of the random vector
Let's say I have $n$ iid random variables $v_i \sim \mathcal{N}(0,c)$ with $c$ is a constant, and put them into a vector: $V=\begin{bmatrix}
v_1\\
v_2\\
...\\
v_n
\end{bmatrix}$. I am interested in ...
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