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Random variables#136

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vishwaksen-1 wants to merge 5 commits into777arc:masterfrom
vishwaksen-1:random-variables
Open

Random variables#136
vishwaksen-1 wants to merge 5 commits into777arc:masterfrom
vishwaksen-1:random-variables

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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.

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