Common Random Variables
Probability, Statistics, and Simulation
Its been quite a while since I’ve written an article and I’ve been eager to return but was uncertain how I should make my grand reentrance. Then I decided uncertainty is exactly how — in this article I will be discussing common random variables.
Everybody wants to build artificially intelligent models but nobody wants to work on or study basic probability and statistics. I won’t even mention the dreaded data collection, cleaning, and preprocessing.
Nevertheless, these ideas are fundamental to the problem space.
This article is to serve as a technical guide to random variables which are inextricably linked to probability.
Executive Summary
Random variables are a function acting on a set called the sample space, if the cardinality of the set is finite or countably infinite then the random variable is discrete, otherwise, it is continuous.
Kolmogorov’s axioms of probability provide a basis for consistent measurement, some choose to relax these axioms but the three ideas reduce to
- probability is bound between zero and one
- probability of something occurring is 1
- disjoint event probability is additive
