Problem 30
Simpson's Paradox (1951)
Problem. Consider the three events X, Y, and Z. Suppose
Prove that it is still possible to have
Solution. Using the law of total probability, we have
where 
and 
. Therefore,
We now consider the sign of Eq. (30.3). Let 
, 
, and 
. Then
where . Therefore, is negative if .
The algebra can mask the real implication of the three ...
Get Classic Problems of Probability now with the O’Reilly learning platform.
O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.
Get Mark Richards’s Software Architecture Patterns ebook to better understand how to design components—and how they should interact.
Dive in for free with a 10-day trial of the O’Reilly learning platform—then explore all the other resources our members count on to build skills and solve problems every day.
Start your free trial Become a member now
