STAT 410
Examples for 10/07/2009
Fall 2009
1.
Suppose that company A and company B are in the same industry sector, and the
prices of their stocks, $X per share for company A and $Y per share for company
B, vary from day to day randomly according to a bivariate normal distribution
with parameters
μ
X
= 45,
σ
X
= 5.6,
μ
Y
= 25,
σ
Y
= 5,
ρ
= 0.8.
a)
What is the probability that on a given day the price of stock for company B
(
Y
)
exceeds $33?
Y
has Normal distribution with mean
μ
Y
= 25
and
standard deviation
σ
Y
= 5.
P
(
Y > 33
)
=

5
25
33
Z
P
=
P
(
Z > 1.60
)
=
1 –
Φ
(
1.60
)
=
1 – 0.9452
=
0.0548
.
b)
Suppose that on a given day the price of stock for company A
(
X
)
is $52.
What
is the probability that the price of stock for company B
(
Y
)
exceeds $33?
Given
X = 52,
Y
has Normal distribution
with mean
( 29
X
X
Y
Y
μ
σ
σ
ρ
μ

+
x
=
( 29
45
52
6
.
5
5
8
.
0
25

+
⋅
⋅
=
30
and
variance
( 29
2
Y
2
σ
ρ
1
⋅

=
( 29
2
2
5
8
.
0
1
⋅

=
9
( standard deviation =
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 Fall '08
 Monrad
 Normal Distribution, Standard Deviation

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