Building on the probability fundamentals from the previous chapter, we now focus on specific mathematical functions that describe the likelihood of different outcomes for random variables: probability distributions. These distributions are fundamental tools for modeling the uncertainty inherent in data, a common task in machine learning.

This chapter introduces several common distributions used frequently in statistical analysis and as building blocks for ML models. You will learn to:

• Identify and describe key discrete distributions: Bernoulli, Binomial ($n, p$), and Poisson ($\lambda$).
• Identify and describe key continuous distributions: Uniform, Normal ($\mu, \sigma^2$), and Exponential ($\lambda$).
• Understand the properties that make each distribution suitable for modeling specific types of data or phenomena.
• Apply Python libraries, particularly SciPy, to compute probabilities (like probability density/mass functions and cumulative distribution functions), generate random samples, and visualize these distributions.

By the end of this chapter, you will be equipped to recognize and utilize these standard distributions when analyzing data and understanding statistical methods employed in machine learning.