Chapter 4. Continuous Random Variables

Table of Contents

• From Discrete to Continuous
• Continuous Random Variables
• Probability Density Function
• Expectation
• Moments and Variance
• Cumulative Distribution Function
• Mean, Median and Mode
• Continuous Uniform Distribution
• Exponential Distribution
• Gaussian Distribution
• Skewness and Kurtosis
• Convolution and Sum of Random Variables
• Functions of Random Variables

This chapter extends the concepts of probability theory to continuous random variables. We will first introduce the concept of probability density function and then discuss the properties of continuous random variables. We will also discuss the concept of cumulative distribution function and its properties.

We will also discuss some common continuous random variables, including the uniform distribution, the exponential distribution, and the normal distribution.