STA 112 Basic Probability Distribution Functions

Description

This academic note, designed for introductory probability students, introduces fundamental concepts of probability distribution functions. It comprehensively covers four essential distributions: Binomial, Geometric, Poisson, and Normal. For each distribution, the material provides definitions, details on their respective Probability Mass Functions (PMF) or Probability Density Functions (PDF), and formulas for calculating mean and variance. Numerical examples illustrate the application of these distributions in various real-life scenarios, including engineering, environmental, and experimental contexts. The document also highlights key properties differentiating discrete (Binomial, Geometric, Poisson) from continuous (Normal) distributions. This resource is suitable for students seeking a foundational understanding of modeling random phenomena.