0
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1answer
41 views

subscript notation in conditional probability

$X$ and $Y$ are two discrete random variables with joint p.m.f $p_{XY}$ such that $p_{XY}(x_i,y_j) = P(X=x_i, Y=y_i)$. I came across a notation that refers to $p_{X}(x|y)$. How do I express it in the ...
1
vote
1answer
75 views

Notation used for multivariate random variables

Let $(\Omega, \mathcal{F}, P)$ be a probability space and $X_1(\omega), \dots, X_n(\omega)$ be random variables defined on the space. Suppose we are concerned with the joint behavior of the variables. ...
0
votes
1answer
16 views

What does it mean to randomly choose an integer from a constant?

In this paper on pg. 1241 under section 2.3 "The Elect Protocol" 2nd paragraph the author says Each party samples a random value $x_i$ from [n/k]. What does that mean? If there are n parties ...
2
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0answers
120 views

Notation for sampling a random variable

my question is pretty much the same as the one asked here: Notation for sampling random variate (I did not find a satisfying answer there...): I have a random variable $X \sim U(1, 10)$. I want to ...
1
vote
0answers
161 views

How to denote a random variable and the set of possible values

I'm curious what the most common way is to denote a random variable and the set of possible values that it can take on. I doesn't seem correct to say, for instance: $r.v.\ X \in \{\ldots\}$, because ...
1
vote
2answers
89 views

What exactly does this physically mean?

Let X(w) be a real random variable on ($\Omega$ , P). The image X($\Omega$) the set of all the values X(w) can take ,written $\Omega^{X}$. For any set $ B \subset \Omega^{X}$ the probability of the ...
2
votes
1answer
217 views

How a random variable takes a value?

Why do mathematicians say a random variable takes on a value? Is it just for convenience? My understanding is that a random variable is a function mapping the sample space of an experiment to a ...