2
(1) (7) The joint mass function for random variables X and Y is in the following table:
p(x,y)
X= 5
X=5
X=10
Y=10
0
.
05
0
.
15
0
.
2
Y=20
0
.
15
0
.
10
0
.
35
(a) (1) Compute the marginal mass functions
p
X
(
x
)
and
p
Y
(
y
)
(b) (2) Compute
E
(
X
)
and
V
(
X
)
(c) (2) Compute
E
(
Y
)
and
V
(
Y
)
(d) (1) Compute Cov
(
X, Y
)
(e) (1) Compute Corr
(
X, Y
)
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3
(2) (6) Assume the temperature in July across the country follow a Normal distribution with mean
80
o
F and
variance 25.
(a) (1) What’s the probability a randomly selected county’s July temperature is between
85
o
F and
100
o
F?
(b) (1) What’s the probability a randomly selected county’s July temperature is between
70
o
F and
90
o
F?
(c) (1.5) If a researcher plans to randomly sample
16
counties, what’s the probability that average July
temperature of the
16
counties is between
76
.
5
o
F and
81
.
5
o
F?
(d) (1.5) Later
16
counties have been randomly selected and their July temperatures measured.
The
average temperature is
78
.
6
o
F. Assume the researcher does not know the actual population mean, but
he knows variance is 25. Construct a
99%
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 Spring '08
 Staff
 Normal Distribution, Probability theory, probability density function, $50, $400, randomly selected county

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