Random Variable

Instance of: measurable function

AKA: random quantity, aleatory variable, or stochastic variable

Distinct from:

English: A variable which takes values from a sample space, where a probablity distribution describes which values/sets of values are more likely to be taken.

Formalization:

A random variable is just a function mapping outcomes to some measurement space. \[ X:\Omega \mapsto E \]

The measurement space is usually the reals, \(\mathbb{R}\). The outcomes are formally supposed to be probability spaces, which are defined as triples \((\omega, \mathcal{F}, P)\). Where \(\mathcal{F}\) could be sets of more than 1 of the possible outcomes, and \(P\) maps each possible set to a 0-1 probaility.

\[ P(X \in S)=P({\omega\in \Omega| X(\omega) \in S}) \]

Cites: Wikipedia ; Wikidata ; Wolfram

Code

Examples:

library(DBI)
# Create an ephemeral in-memory RSQLite database
#con <- dbConnect(RSQLite::SQLite(), dbname = ":memory:")
#dbListTables(con)
#dbWriteTable(con, "mtcars", mtcars)
#dbListTables(con)

#Configuration failed because libpq was not found. Try installing:
#* deb: libpq-dev libssl-dev (Debian, Ubuntu, etc)
#install.packages('RPostgres')
#remotes::install_github("r-dbi/RPostgres")
#Took forever because my file permissions were broken
#pg_lsclusters
require(RPostgres)

Loading required package: RPostgres

# Connect to the default postgres database
#I had to follow these instructions and create both a username and database that matched my ubuntu name
#https://www.digitalocean.com/community/tutorials/how-to-install-postgresql-on-ubuntu-20-04-quickstart
con <- dbConnect(RPostgres::Postgres())

import torch