Probability, Random Variables, and Selectivity

TL;DR

This chapter introduces a comprehensive Kolmogorovian framework for understanding random variables and joint distributions under different conditions, emphasizing the coupling of variables recorded under mutually exclusive scenarios.

Contribution

It presents a systematic theory of random variables and joint distributions that accommodates coupling under mutually exclusive conditions, expanding traditional probability models.

Findings

Provides a unified Kolmogorovian approach to random variables

Clarifies how joint distributions can be constructed via coupling

Addresses the treatment of mutually exclusive conditions in probability theory

Abstract

This is a chapter for the forthcoming New Handbook of Mathematical Psychology, to be published by Cambridge University Press. A systematic theory of random variables and joint distributions under varying conditions is presented. This is a Kolmogorovian theory most generally understood, in which random variables recorded under mutually exclusive conditions do not possess joint distributions but can be coupled in multiple ways.