<p>By ChatGPT: In the notation E[|S|], the expression |S| denotes the cardinality or the number of elements in the set S. So, E[|S|] means the expected value of the number of elements in the set S.</p>
<p>On the other hand, the notation E[formula] refers to the expected value of a random variable defined by the formula. For example, if the formula is X + Y, where X and Y are random variables, then E[X + Y] represents the expected value of the sum of X and Y.</p>
<p>Regarding the notation E[X], where X∈N, it means the expected value of a discrete random variable X that takes non-negative integer values. In other words, E[X] represents the average value of X when X can only take on values of 0, 1, 2, and so on.</p>

CC BY-SA 4.0
2023-03-30T19:52:47.473Z
2023-03-30T19:52:47.473Z
domotorp
<p>I was reading a paper, and I found a notation that I don't understand:
<span class="math-container">$\mathbb{E}[| \textbf{S} |] $</span>, where <span class="math-container">$\textbf{S}$</span> is a set. Are there any differences with the notation <span class="math-container">$\mathbb{E}[formula]$</span> (I always read this notation like the set of edges such that the formula is true for the edges).
Moreover, what does the notation <span class="math-container">$\mathbb{E}[\textbf{X}]$</span>, where <span class="math-container">$\textbf{X} \in \mathbb N$</span>, mean?</p>
<p>Thank you for your help.</p>

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2023-03-30T19:24:52.897Z
$\mathbb E[X]$ denotes the expected value of a random variable $X$.
Emil Jeřábek
<graph-theory><notation>
notation in graph theory
Palerme
# notation in graph theory

(Asked by: username_0 on 2023-03-30)

I was reading a paper, and I found a notation that I don't understand:
$\mathbb{E}[| \textbf{S} |] $, where $\textbf{S}$ is a set. Are there any differences with the notation $\mathbb{E}[formula]$ (I always read this notation like the set of edges such that the formula is true for the edges).
Moreover, what does the notation $\mathbb{E}[\textbf{X}]$, where $\textbf{X} \in \mathbb N$, mean?

Thank you for your help.

**Tags:** graph-theory, notation

> **Comments:**
> **username_1**: $\mathbb E[X]$ denotes the expected value of a random variable $X$.  

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## 1 answers

### Answer by username_2 on 2023-03-30. Score: 4

By ChatGPT: In the notation E[|S|], the expression |S| denotes the cardinality or the number of elements in the set S. So, E[|S|] means the expected value of the number of elements in the set S.

On the other hand, the notation E[formula] refers to the expected value of a random variable defined by the formula. For example, if the formula is X + Y, where X and Y are random variables, then E[X + Y] represents the expected value of the sum of X and Y.

Regarding the notation E[X], where X∈N, it means the expected value of a discrete random variable X that takes non-negative integer values. In other words, E[X] represents the average value of X when X can only take on values of 0, 1, 2, and so on.


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