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Part B: Statistics
Answer 3 of the following 4 questions.
Q1 The joint probabilities of two random variables (
S
and
T
) are given
in the table below.
S
is the annual percent return on stocks and
T
is
the annual percent return on Treasury Bills.
S
T
10%
0
10%
20%
6%
0
0
.10
.10
8%
0
.10
.30
.20
10%
.10
.10
0
0
Suppose that you have $10,000 to invest.
(a) What would be your expected return if you invested only in
stocks? What would be the variance of your return?
(b) What would be your expected return if you invested only in Trea
sury bills? What would be the variance of your return?
(c) Compare the above two cases to the situation where your invested
half of you wealth in each of stocks and Tresury bills?
(d) Deﬁne the term ‘independence’. Are
S
and
T
independent? Does
this help explain the above pattern of results?
Hint: The hard part is the third case above. The ﬁrst two cases only
require marginal distributions. When answering part c, just think
about what are the events (pairs of returns), what are the probabilities
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 Summer '09
 Smith

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