This preview shows page 1. Sign up to view the full content.
Unformatted text preview: plain why the assumption is important. Problem 2 (14 pts). This problem deals with positive random variables that may
get the value ∞. Let
be a random variable defined on a probability space
. Let ℱ⊂ be a σalgebra. Prove
a. (6 points)
(i)
ℱ
(ii).
ℱ and
(Namely, we can write exist, and
,
)
ℱ ℱ b. (8 points)
If
is a random variable that satisfy (ii) of part a, namely:
,
ℱ then ℱ and Problem 3 (18 pts). Let
be a sequence of integrable random
variables defined on
ℱ
and let ℱ be an increasing seq...
View
Full
Document
This document was uploaded on 03/01/2014 for the course STATS 400 at Michigan State University.
 Spring '12
 STAFF
 Probability

Click to edit the document details