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Statistics 5101, Fall 2010: Homework
Assignment 4
Solve each problem. Explain your reasoning. No credit for answers with no
explanation. If the problem is a proof, then you need words as well as formulas.
Explain why your formulas follow one from another.
41.
If
U
,
V
,
X
, and
Y
are any random variables, show that
cov(
U
+
V,X
+
Y
) = cov(
U,X
) + cov(
V,X
) + cov(
U,Y
) + cov(
V,Y
)
42.
Suppose
X
1
,
X
2
,
X
3
are IID with mean
μ
and variance
σ
2
. Calculate the
mean vector and variance matrix of the random vector
Y
=
Y
1
Y
2
Y
3
=
X
1

X
2
X
2

X
3
X
3

X
1
43.
Suppose
X
and
Y
are independent random variables, with means
μ
X
and
μ
Y
, respectively, and variances
σ
2
X
and
σ
2
Y
, respectively. Calculate
E
(
X
2
Y
2
)
in terms of
μ
X
,
μ
Y
,
σ
2
X
, and
σ
2
Y
.
44.
Suppose 6 balls that are indistinguishable except for color are placed in
an urn and suppose 3 balls are red and 3 are white. Suppose 2 balls are drawn.
What is the probability the one is red and the other white under each of the
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This note was uploaded on 12/01/2010 for the course STAT 5101 taught by Professor Staff during the Fall '02 term at Minnesota.
 Fall '02
 Staff
 Statistics

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