# The necessities in Random Processes

## Random Variables

### The Random Variable

• The Random Variable (A.pdf)
• Distribution Function (A.pdf)
• Density Function (A.pdf)
• The Gaussian Random Variable (A.pdf, B.pdf)
• Other Distribution and Density Functions (A.pdf)
• Conditional Distribution and Density Functions (A.pdf)

### Multiple Random Variables

• Vector Random Variables (A.pdf)
• Joint Distribution (A.pdf)
• Joint Density (A.pdf)
• Conditional Joint Distribution and Density (A.pdf)
• Statistical Independence (A.pdf)
• Sums of Random Variables (A.pdf)
• Central Limit Theorem (A.pdf)

### The Characteristics of Multiple Random Variables

• Expected Values (A.pdf)
• Joint Characteristic Functions (A.pdf)
• Jointly Gaussian Random Variables (A.pdf)
• Transformations of Multiple Random Variables (A.pdf)
• Linear Transformation of Gaussian Random Variables (A.pdf)
• Simulating Multiple Random Variables (A.pdf)
• Sampling and Some Limit Theorem (A.pdf)
• Complex Random Variables (A.pdf)

## Random Processes

### The Temporal Characteristics of Random Processes

• The Random Process (A.pdf)
• Joint Distribution, Independence, Processes (A.pdf)
• Stationarity (A.pdf)
• Example Random Processes (A.pdf)
• Time Averages and Ergodicity (A.pdf)
• Measurement of Correlation Functions
• Complex Random Processes

### The Spectral Characteristics of Random Processes

• Power Density Spectrum - Continuous Time
• Auto Correlation Function
• Power Density Spectrum - Discrete Time
• Cross Power Density Spectrum
• Cross Correlation Function
• Noise Definitions
• Power Spectrum of Complex Random Processes

## Correlation and Power Spectra

1. Correlation Functions of Random Signals (pdf)
2. Spectra of Random Signals (pdf)

## Random Processes and Linear Systems

1. Time Domain Techniques for Noisy Signals (A.pdf, B.pdf)
2. Frequency Domain Techniques for Noisy Signals
3. Correlation v.s. Convolution for Noisy Signals

1. System Identification (pdf)
2. Matched Filter 

1. Understanding Digital Communications, See Baseband Mod/Demod Section