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
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