This preview shows page 1. Sign up to view the full content.
Unformatted text preview: e that the variance of the uniform distribution
will only depend on the length of the interval. To see that it will be a multiple
of (b a)2 note that Z = X/(b a) is uniform on [ 1/2, 1/2] and then use part
(d) of Theorem A.3 to conclude var (X ) = (b a)2 var (Z ). Of course one needs
calculus to conclude that var (Z ) = 1/12.
Generating functions will be used at several points in the text. If pk =
P (X = k ) is the distribution of X then the generating function is (x) =
(1) = k=0 pk = 1. Di↵erentiating (and not worrying about the
k=0 pk x .
detail of interchanging the sum and th...
View Full Document
This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell University (Engineering School).
- Spring '10
- The Land