Kata Bognar
[email protected]
Economics 41
Statistics for Economists
UCLA
Fall 2010
Midterm 2
 suggested solutions by Minji Kang 
Part I  Multiple Choice Questions (4 points each)
1. Chebyshev’s theorem is applicable to:
B
(a) bellshaped distributions only
(b)
any kind of distribution
(c) continuous distributions only
(d) discrete distributions only
2. A professor responds to student questions by email. The following table describes the number of
emails that the professor may receive from the students each day.
number of emails
probability
0
0.05
1
0.1
2
0.2
3
0.25
4
0.3
5
0.1
It takes the professor 10 minutes to respond each email. How much time should the professor
expect to spend responding emails per day?
C
(a) 9.5
(b) 2.95
(c)
29.5
(d) none of the above
Explanation:
Denote by
X
the number of emails the professor receives per day. Then
E
[
X
] =
0(0
.
05)+1(0
.
1)+2(0
.
2)+3(0
.
25)+4(0
.
3)+5(0
.
1) = 2
.
95
.
Since answering an email takes 10 minutes,
the expected time the professor spends with responding to emails is
E
[10
X
] = 10
E
[
X
] = 29
.
5
.
3. The American Veterinary association claims that the annual costs of medical care for dogs has
a mean of $100 and a variance of 30, while the annual costs of medical care for cats has a mean
of $120 and a variance of 35. Suppose that a person has a cat and a dog and no other pets.
Also assume that the need for medical care for the dog and for the cat is independent. Then this
person
D
(a) expects to spend $220 on medical care for his/her pets with a variance of 75.
(b) expects to spend $120 on medical care for his/her pets with a variance of 30.
(c) expects to spend $100 on medical care for his/her pets with a variance of 30.
(d)
none of the above is true
Explanation:
Denote by
X
the annual cost of medical care for a dog and by
Y
the annual
cost of medical care for a cat. Then the total costs of medical care for both pets is
X
+
Y.
It is given that
E
[
X
] = 100
,E
[
Y
] = 120
,V ar
[
X
] = 30 and
V ar
[
Y
] = 35
.
Using the formulas
E
[
X
+
Y
] =
E
[
X
] +
E
[
Y
] and
V ar
[
X
+
Y
] =
V ar
[
X
] +
V ar
[
Y
]
,
one gets that the expected value
of total medical costs is $220 with a variance of 65.
1
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View Full Document4. The maximum likelihood estimate is
C
(a) a random variable
(b) a function of random variables
(c)
a value of a statistic
(d) a statistic
Explanation:
See deﬁnitions in the book / slides.
5.
X
is a random variable with a p.d.f
f
(
x
) =
a
(3

x
) for 1
< x <
3 where
a
is a constant. Then
the expected value of
X
is
B
(a) 1/2
(b)
5/3
(c) 1
(d) none of the above
Explanation:
Since
f
(
x
) is a density function,
R
3
1
a
(3

x
)d
x
= 1
.
This implies that
a
=
1
2
.
Then
E
[
X
] =
R
3
1
x
1
2
(3

x
)d
x
=
5
3
.
6. Determine whether the following random variable has a binomial distribution. If not, state the
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 Fall '07
 Guggenberger
 Economics, Normal Distribution, Standard Deviation, Probability theory, medical care, p.m.f.

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