= 27d567bc2d48d9f40e9ccc20ea370b15)
prase comments on Causality does not imply correlation - Less Wrong
You are viewing a comment permalink. View the original post to see all comments and the full post content.
= 783df68a0f980790206b9ea87794c5b6)
Loading…= b715d02e85f7b3b4ae65ca3d3e450868)
Subscribe to RSS Feed
Powered by Reddit
= f037147d6e6c911a85753b9abdedda8d)
You are viewing a comment permalink. View the original post to see all comments and the full post content.
Comments (54)
The standard form for correlation coefficient is
cov(x,y)=N(<xy>-<x><y>)
where N is normalisation; it seems that you suppose that <f>=0 and <f'> finite, then. <f>=0 follows from boundedness, but for the derivative it's not clear. If <f'> on (a,b) grows more rapidly than (b-a), anything can happen.
This cannot happen. f is assumed bounded. Therefore the average of f' over the interval [a,b] tends to zero as the bounds go to infinity.
The precise, complete mathematical statement and proof of the theorem does involve some subtlety of argument (consider what happens if f = sin(exp(x))) but the theorem is correct.