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In the last paragraph I explain my own opinion.

### Introduction

The article starts with the following sentence.

### 2.1 Simple example

 Probability P(z) Value z 1/4 1+i 1/4 1-i 1/2 2
Consider a random variable that may take only the three complex values 1 + i , 1 - i , 2 with probabilities as specified in the table.
This is a simple example of a complex random variable.
The expectation of this random variable may be simply calculated:
E[Z] = 1/4(1+i) + 1/4 (1-i) =1/2*2 = 3/2
This works because the probabilities in line 1 and 2 are identical. If not the calculated expectation value would be a complex number, and what would that mean?

### 2.2 Uniform distribution

Another example of a complex random variable is the uniform distribution over the filled unit circle, i.e. the set { z inclusif C | |z| = 1 } This random variable is an example of a complex random variable for which the probability density function is defined.
Tricky to compare within the real world

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Created: 11 January 2022

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