F2006
F2006

RANDOM VARIABLES Definition: Recall that a probability space (S
RANDOM VARIABLES Definition: Recall that a probability space (S

Introduction to Probability Distributions
Introduction to Probability Distributions

PDF
PDF

DENSITY NOTATION 1. densities Let X be a random variable on (Ω
DENSITY NOTATION 1. densities Let X be a random variable on (Ω

... expectation E{X|Y = y} = h(y). We might want to extend this definition into a more ...

Conditioning (probability)

Beliefs depend on the available information. This idea is formalized in probability theory by conditioning. Conditional probabilities, conditional expectations and conditional distributions are treated on three levels: discrete probabilities, probability density functions, and measure theory. Conditioning leads to a non-random result if the condition is completely specified; otherwise, if the condition is left random, the result of conditioning is also random.This article concentrates on interrelations between various kinds of conditioning, shown mostly by examples. For systematic treatment (and corresponding literature) see more specialized articles mentioned below.