Random variables

[vishwaksen-1]

Summary

This PR adds a new standalone chapter on Random Variables and Random Processes and improves the mobile rendering of the Detection chapter.

Changes

1. New Random Variables Chapter

Added content/random_variables.rst - a comprehensive introduction to random variables and random processes, covering:

• What random variables are (single sample vs. many samples)
• Probability distributions (focus on Gaussian)
• Expectation (mean) and variance
• Scaling and shifting random variables
• Complex random variables and complex Gaussian noise
• Random processes and stationarity
• Practical Python examples throughout

This chapter provides foundational material that can be referenced or integrated before the Noise chapter. It addresses the confusion mentioned in #120 about variance, power, and the difference between a single random sample and a collection of samples.

2. Detection Chapter Improvement

Replaced the manually-drawn ASCII flowchart in content/detection.rst with a Mermaid diagram for better rendering on mobile devices and tablets.

3. Supporting Files

• Added figure generation script for Gaussian distribution histogram
• Generated figures for the Random Variables chapter

Integration Notes

The Random Variables chapter is intentionally kept standalone to allow @777arc to decide:

• Which sections to use
• Where to integrate it (likely before the Noise chapter)
• Whether to merge it with existing content or keep it separate

P.S. I might've messed up my forked repository and hence it's still including the previous commits along with this commit, please don't mind.

[vishwaksen-1]

Hi @777arc! In this PR, I tried replacing the flowchart with mermaid chart in "Detection using Correlation" part that I wrote earlier, as I thought it would render better in all devices; and hence added sphinx- mermaid library in conf.py, but it seems that this library is what's caused the check failure.

[777arc]

Awesome contribution, for the mermaid error that's just because I have to add it as a pip install. I'm going to incorporate this into the Noise chapter in a separate branch