-- card: 10173 from stack: in
-- bmap block id: 8952
-- flags: 0000
-- background id: 2595
-- name: 


-- part contents for background part 22
----- text -----
Given an approximate map ƒ, a lot of analysis can be done to produce sharp estimates for various aspects of ƒ,  which then approximate those of the exact  F.

Suppose        is some quantity of interest.
•  The long-term average


•  A direct estimate from data is

     with error