There are three items I wish to bring to the reader's attention.
Issue 2
Suppose we have two quantities, $x$ and $y$, and we are given that $y$ may be expressed as an infinite power series in $x$:
$$ y = a_1 x + a_2x^2 + a_3x^3 + \cdots$$
Issue 3
In probability theory and in everyday language we use the word 'random' and, for many of us, our first encounter with the word would have been in drawing a name at random from a hat.