Introduction to Econometrics (Global Edition)
4e James Stock, Mark Watson (Test Bank)
Introduction to Econometrics, 4e (Stock/Watson)
Chapter 2 Review of Probability
2.1 Multiple Choice Questions
1) The probability of an outcome:
A) is the number of times that the outcome occurs in the long run.
B) equals M × N, where M is the number of occurrences and N is the population size.
C) is the proportion of times that the outcome occurs in the long run.
D) equals the sample mean divided by the sample standard deviation.
Answer: C
2) The probability of an event A or B (Pr(A or B)) to occur equals:
A) Pr(A) × Pr(B).
B) Pr(A) + Pr(B) if A and B are mutually exclusive.
C)
.
D) Pr(A) + Pr(B) even if A and B are not mutually exclusive.
Answer: B
3) The cumulative probability distribution shows the probability:
A) that a random variable is less than or equal to a particular value.
B) of two or more events occurring at once.
C) of all possible events occurring.
D) that a random variable takes on a particular value given that another event has
happened.
Answer: A
4) The expected value of a discrete random variable:
A) is the outcome that is most likely to occur.
B) can be found by determining the 50% value in the c.d.f.
C) equals the population median.
D) is computed as a weighted average of the possible outcome of that random variable,
where
the weights are the probabilities of that outcome.
Answer: D
5) Let Y be a random variable. Then var(Y) equals:
A)
.
B) E
.
C) E
.
,D) E
.
Answer: C
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6) The skewness of the distribution of a random variable Y is defined as follows:
A)
B) E
C)
D)
Answer: D
7) The skewness is most likely positive for one of the following distributions:
A) The grade distribution at your college or university.
B) The U.S. income distribution.
C) SAT scores in English.
D) The height of 18 year old females in the U.S.
Answer: B
8) The kurtosis of a distribution is defined as follows:
A)
B)
C)
D) E[(Y -
)4)
Answer: A
9) For a normal distribution, the skewness and kurtosis measures are as follows:
A) 1.96 and 4
B) 0 and 0
C) 0 and 3
D) 1 and 2
Answer: C
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10) The conditional distribution of Y given X = x, Pr(Y = y =x), is:
A)
.
B)
C)
,D)
.
Answer: D
11) The conditional expectation of Y given X, E(Y
, is calculated as follows:
A)
B) E
C)
D)
Pr(X = xi)
Answer: C
12) Two random variables X and Y are independently distributed if all of the following
conditions hold, with the exception of:
A) Pr(Y = y = x) = Pr(Y = y).
B) knowing the value of one of the variables provides no information about the other.
C) if the conditional distribution of Y given X equals the marginal distribution of Y.
D) E(Y) = E[E(Y )].
Answer: D
13) The correlation between X and Y:
A) cannot be negative since variances are always positive.
B) is the covariance squared.
C) can be calculated by dividing the covariance between X and Y by the product of the two
standard deviations.
D) is given by corr(X, Y) =
.
Answer: C
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14) Two variables are uncorrelated in all of the cases below, with the exception of:
A) being independent.
B) having a zero covariance.
C)
D) E(Y
) = 0.
Answer: C
15) var(aX + bY) =
A)
+
.
B)
, + 2ab
+
.
C)
+
.
D) a
+b
.
Answer: B
16) To standardize a variable you:
A) subtract its mean and divide by its standard deviation.
B) integrate the area below two points under the normal distribution.
C) add and subtract 1.96 times the standard deviation to the variable.
D) divide it by its standard deviation, as long as its mean is 1.
Answer: A
17) Assume that Y is normally distributed N(μ, σ2). Moving from the mean ( μ) 1.96
standard
deviations to the left and 1.96 standard deviations to the right, then the area under the
normal
p.d.f. is:
A) 0.67
B) 0.05
C) 0.95
D) 0.33
Answer: C
18) Assume that Y is normally distributed N(μ, σ2). To find Pr( ≤ Y ≤ ), where < and di =
, you need to calculate Pr(
≤Z≤
)=
A) Φ(
) - Φ(
)
B) Φ(1.96) - Φ(1.96)
C) Φ(
) - (1 - Φ(
))
D) 1 - (Φ(
) - Φ(
))
Answer: A
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4e James Stock, Mark Watson (Test Bank)
Introduction to Econometrics, 4e (Stock/Watson)
Chapter 2 Review of Probability
2.1 Multiple Choice Questions
1) The probability of an outcome:
A) is the number of times that the outcome occurs in the long run.
B) equals M × N, where M is the number of occurrences and N is the population size.
C) is the proportion of times that the outcome occurs in the long run.
D) equals the sample mean divided by the sample standard deviation.
Answer: C
2) The probability of an event A or B (Pr(A or B)) to occur equals:
A) Pr(A) × Pr(B).
B) Pr(A) + Pr(B) if A and B are mutually exclusive.
C)
.
D) Pr(A) + Pr(B) even if A and B are not mutually exclusive.
Answer: B
3) The cumulative probability distribution shows the probability:
A) that a random variable is less than or equal to a particular value.
B) of two or more events occurring at once.
C) of all possible events occurring.
D) that a random variable takes on a particular value given that another event has
happened.
Answer: A
4) The expected value of a discrete random variable:
A) is the outcome that is most likely to occur.
B) can be found by determining the 50% value in the c.d.f.
C) equals the population median.
D) is computed as a weighted average of the possible outcome of that random variable,
where
the weights are the probabilities of that outcome.
Answer: D
5) Let Y be a random variable. Then var(Y) equals:
A)
.
B) E
.
C) E
.
,D) E
.
Answer: C
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6) The skewness of the distribution of a random variable Y is defined as follows:
A)
B) E
C)
D)
Answer: D
7) The skewness is most likely positive for one of the following distributions:
A) The grade distribution at your college or university.
B) The U.S. income distribution.
C) SAT scores in English.
D) The height of 18 year old females in the U.S.
Answer: B
8) The kurtosis of a distribution is defined as follows:
A)
B)
C)
D) E[(Y -
)4)
Answer: A
9) For a normal distribution, the skewness and kurtosis measures are as follows:
A) 1.96 and 4
B) 0 and 0
C) 0 and 3
D) 1 and 2
Answer: C
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10) The conditional distribution of Y given X = x, Pr(Y = y =x), is:
A)
.
B)
C)
,D)
.
Answer: D
11) The conditional expectation of Y given X, E(Y
, is calculated as follows:
A)
B) E
C)
D)
Pr(X = xi)
Answer: C
12) Two random variables X and Y are independently distributed if all of the following
conditions hold, with the exception of:
A) Pr(Y = y = x) = Pr(Y = y).
B) knowing the value of one of the variables provides no information about the other.
C) if the conditional distribution of Y given X equals the marginal distribution of Y.
D) E(Y) = E[E(Y )].
Answer: D
13) The correlation between X and Y:
A) cannot be negative since variances are always positive.
B) is the covariance squared.
C) can be calculated by dividing the covariance between X and Y by the product of the two
standard deviations.
D) is given by corr(X, Y) =
.
Answer: C
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14) Two variables are uncorrelated in all of the cases below, with the exception of:
A) being independent.
B) having a zero covariance.
C)
D) E(Y
) = 0.
Answer: C
15) var(aX + bY) =
A)
+
.
B)
, + 2ab
+
.
C)
+
.
D) a
+b
.
Answer: B
16) To standardize a variable you:
A) subtract its mean and divide by its standard deviation.
B) integrate the area below two points under the normal distribution.
C) add and subtract 1.96 times the standard deviation to the variable.
D) divide it by its standard deviation, as long as its mean is 1.
Answer: A
17) Assume that Y is normally distributed N(μ, σ2). Moving from the mean ( μ) 1.96
standard
deviations to the left and 1.96 standard deviations to the right, then the area under the
normal
p.d.f. is:
A) 0.67
B) 0.05
C) 0.95
D) 0.33
Answer: C
18) Assume that Y is normally distributed N(μ, σ2). To find Pr( ≤ Y ≤ ), where < and di =
, you need to calculate Pr(
≤Z≤
)=
A) Φ(
) - Φ(
)
B) Φ(1.96) - Φ(1.96)
C) Φ(
) - (1 - Φ(
))
D) 1 - (Φ(
) - Φ(
))
Answer: A
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