Distinguishing variables from parameters

This article clarifies the often confusing distinction between variables and parameters in mathematical functions and programming contexts. It uses a dialogue between a professor and student to illustrate how parameters are fixed in a given application but vary across applications, while variables are free to change within a context. The author discusses notation like semicolons and vertical bars to separate variables from parameters, providing examples from probability density functions and hypergeometric functions. The article emphasizes that while technically both are variables, the distinction is practically useful for understanding how functions behave and are applied in fields like statistics and software development.