I'm having trouble with the machine learning vocabulary, especially with the concept of random variables.
Given a sample $X$ (with features $x_1, x_2, \dots, x_n$) that you train your algorithm on (or predict), what is the random variable? Is it $X$? Or is it any of its feature $x_1, x_2, \dots, x_n$?
Quoting The Deep Learning book (by Ian Goodfellow):
A random variable is a variable that can take on different values randomly. We typically denote the random variable itself with a lowercase letter in plain typeface
Where as in the definition of a Random Variable in the Wikipedia article:
A random variable is a measurable function from a set of possible outcomes to a measurable space E
Then we also have the definition of multivariate random variable
A multivariate random variable is a column vector (or its transpose, which is a row vector) whose components are scalar-valued random variables on the same probability space as each other.
Should a sample be in fact considered as a multivariate random variable?