STAT 410
Fall 2011
Homework #5
(due Friday, October 7, by 3:00 p.m.)
1.
Every month, the government of Neverland spends X million dollars purchasing guns and
Y million dollars purchasing butter.
Assume X and Y jointly follow a Bivariate Normal
distribution with parameters
μ
X
= 370,
σ
X
= 50,
μ
Y
= 270,
σ
Y
= 40,
ρ
= – 0.80.
a)
Suppose the government of Neverland spent 450 million dollars on guns during a
particular month.
Find the probability that more than 250 million was spent on butter
during the same month.
That is, find
P
(
Y > 250

X = 450
).
b)
Find the probability that the government of Neverland spends more on guns than on
butter during a given month.
That is, find
P
(
X > Y
).
c)
Find the probability that the government of Neverland exceeds the 700million spending
limit during a given month.
That is, find
P
(
X + Y > 700
).
2.
For a certain population, the blood pressure
(
X
, Y
) = (
systolic
, diastolic
) can be
modeled as having a bivariate normal distribution with
μ
X
= 120,
σ
X
= 20,
μ
Y
= 82,
σ
Y
= 15,
ρ
= 0.6.
a)
Find the probability that an individual with a diastolic pressure
(
Y
) of 91 will
have a systolic pressure
(
X
) exceeding 140.
That is, find
P
(
X > 140

Y = 91
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 Fall '08
 Monrad
 Statistics, Normal Distribution, Probability, Standard Deviation, Variance, bivariate normal distribution, The Queen

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