Functions related to probability distributions

Probability distributions are mathematical functions that provide a description of the likelihood of different outcomes in a random experiment. They are fundamental to the field of probability and statistics. Functions related to probability distributions can be classified into several categories, including probability mass functions (PMFs), probability density functions (PDFs), cumulative distribution functions (CDFs), and characterizing functions like moment-generating functions (MGFs) and cumulant-generating functions (CGFs). Here's a brief overview of these functions: ### 1.