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UCSD ECE 153
Handout #11
Prof. YoungHan Kim
Thursday, October 23, 2008
Homework Set #4
Due: Thursday, October 30, 2008
1. Read Sections 4.3, 4.6, 5.7, 5.9, 6.5 in the text. Try to work on all examples.
2.
Two envelopes.
An amount
A
is placed in one envelope and the amount 2
A
is placed
in another envelope. The amount
A
is ﬁxed but unknown to you. The envelopes are
shuﬄed and you are given one of the envelopes at random. Let
X
denote the amount
you observe in this envelope. Designate by
Y
the amount in the other envelope. Thus
(
X, Y
) =
(
(
A,
2
A
)
,
with probability
1
2
,
(2
A, A
)
,
with probability
1
2
.
You may keep the envelope you are given, or you can switch envelopes and receive the
amount in the other envelope.
(a) Find
E
(
X
) and
E
(
Y
).
(b) Find
E
±
X
Y
)
.
(c) Suppose you switch. What is the expected amount you receive?
3.
Tall trees.
Suppose that the average height of trees on campus is 20 feet. Argue that
no more than half of the tree population is taller than 40 feet.
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This note was uploaded on 10/26/2011 for the course MATH 180C taught by Professor Eggers during the Winter '09 term at Aarhus Universitet.
 Winter '09
 Eggers

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