Measure, Integration & Real Analysis · Problem 12.6

Probability Measures — Sheldon Axler

Mathematics — Measure Theory · pairwise-independent-not-mutually

Problem

Give an example of a probability space

(\Omega, \mathcal{F}, P)

and events

A_1, A_2, A_3

such that

A_1

and

A_2

are independent,

A_1

and

A_3

are independent, and

A_2

and

A_3

are independent, but the family

A_1, A_2, A_3

is not independent.