Chapter Overview
This chapter transitions from discrete to continuous random variables. You'll learn how to work with probability density functions (PDFs), cumulative distribution functions (CDFs), and master important distributions like uniform, exponential, gamma, and normal.
4
Sections
4
Simulators
48
Practice Problems
~25%
Of Exam P
Key Formulas You'll Learn
PDF Properties
f(x) ≥ 0, ∫f(x)dx = 1
CDF Definition
F(x) = P(X ≤ x) = ∫f(t)dt
PDF from CDF
f(x) = F'(x)
Uniform U(a,b)
f(x) = 1/(b-a)
Uniform Mean
μ = (a+b)/2
Uniform Variance
σ² = (b-a)²/12
Mean (Continuous)
μ = ∫x·f(x)dx
Variance (Continuous)
σ² = ∫(x-μ)²f(x)dx
Percentile
F(πp) = p
Sections
3.1 Random Variables of the Continuous Type
Continuous random variables, PDFs, CDFs, and the uniform distribution
3.2 Exponential, Gamma, and Chi-Square
Waiting times, the exponential distribution, and related distributions
3.3 The Normal Distribution
The bell curve, standard normal, and normal approximations
3.4 Additional Models
Beta, Weibull, and other continuous distributions