What is a variable as opposed to a parameter? What is a variable as opposed to a parameter?
I have never seen or heard of a clean definition.
As of my opinion, a parameter is a fixed value, whereas a variable is, deep thought, the result of an undefined function, like it is for "stochastic" variables, minus that "stochastic" prefix.
 A: Mathematical expressions involving many letters and other symbols are often used to define functions, such as
$$ax^2+bx+c.$$
Writing $n$ for the number of distinct letters involved (four in the example above), the domain of the function one has in mind is usually not as big as $\mathbb R^n$, but rather $\mathbb R^m$, where $m$ is the number of a chosen  subset of letters which are called the variables, while all others are called parameters.
Of course, in order to define a concrete function, the parameters must be assigned fixed values, with  different choices leading to different functions.
Speaking of the example above, a popular choice is to call $x$ the variable and $a$, $b$ and $c$ the parameters, but nothing prevents us from making other choices.
A: A parameter is a constant that can be varied if desired. Variables depend on parameters that can be changed.
$$ (x,y)= (2ft,ft^2) $$
is a parabolic curve equation where any point can be associated with a parameter $t$. When $t$ is eliminated we have a single equation $ 4 f y=  x^2. $
Several parameters can be used to distinguish parabolas of different focal lengths $f$.
