Summary: Chapter 7 lecture notes
Math 431, Spring 2011
Instructor: David F. Anderson
Chapter 7: Properties of expectations
Recall that we have
E[X] =
x
xp(x),
in the discrete case and
E[X] =

-
xf(x)dx
in the continuous case.
First useful corollary: If P{a X b} = 1, then
a E[X] b.
Proof.
E[X] =
x:p(x)>0
xp(x) a

Source: Anderson, David F. - Department of Mathematics, University of Wisconsin at Madison

Collections: Mathematics