Probability II
MAP6473 4810
Homework1a
Prof. JLF King
4May2010
Reading.
For Wednesday, 14Jan, please read
Billingsley’s article “The Singular Function of
Bold Play”.
Please get your copy of his text as soon as pos
sible.
Please read Sect.7, pages 92–108 by Monday,
19Jan.
Please read part of Sect.8, pages 111–121 by
Friday, 23Jan.
1a1:
For a random variable
Y
deﬁne
N
(
Y
) :=
Z
Ω
Min(

Y

,
1)
.
Show that
N
(
Y
) = 0
⇐⇒
Y
a.e
= 0
.
Prove or disprove each of the following:
i
:
N
(
Y
) +
N
(
Z
)
>
N
(
Y
+
Z
).
ii
:
If
N
(
Y
n
)
→
0 then
~
Y
converges to 0 in proba
bility.
iii
:
If
~
Y
→
0 in probability, then
N
(
Y
n
)
→
0.
Is
convergenceinprobability
convergence with re
spect to some metric?
1a2:
Consider the following 3state
MC
(Markov
chain) with states
A,B,C
:
State
A
goes to
B
and
C
each with prob=
1
2
.
State
B
goes to states
A,B,C
with probabilities
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 01/26/2012 for the course MAP 6473 taught by Professor King during the Fall '11 term at University of Florida.
 Fall '11
 King

Click to edit the document details