Pstat160A
Winter 2009
Homework #2
Due Friday, January 23
Submit also the Matlab homework assigned on the first week of class
together with part 3.) of question 4 below
Problem 1.
For this problem, you need to read first about covariance, see handout # 1.
A judicious use of the symmetry let you save a lot calculations.
1) Let (
X, Y
) have joint pdf such as each of the 4 points (

1
,
0)
,
(1
,
0)
,
(0
,

1)
,
(0
,
1) have the same probability.
Show that
X
and
Y
are uncorrelated, but are not independent. What is the issue here?
2) Let now (
X, Y
) have joint pdf such as each of the 5 points (

1
,

1)
,
(0
,

1)
,
(0
,
0)
,
(0
,
1)
,
(1
,
1) have the same
probability.
a) Find the covariance and correlation of
X, Y
.
b) Let
Z
= 2
X
. Find the covariance and correlation of
Z, Y
two ways: from the formula relating
X
and
Z
, and
by computing it from their joint pdf.
c) Back in the setup of a), but this time let the points (0
,

1) and (0
,
1) have each probability 1/3, and the other
3 points to be equally likely. Do as in a) and explain the difference with the result found in a).
Problem 2.
Problem 45, chapter 2, p. 91
Use the indicator function trick.
Problem 3.
Problem 61, chapter 2, p.93. Do only
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 Spring '09
 Covariance, Probability theory, Covariance and correlation, matlab homework

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