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Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Be
sure to write your answers in the table provided above
1) The Student t distribution is
A) the distribution of a random variable with a chi-squared distribution with m degrees of freedom,
divided by m.
B) the distribution of the sum of m squared independent standard normal random variables.
C) always well approximated by the standard normal distribution.
D) the distribution of the ratio of a standard normal random variable, divided by the square root of an
independently distributed chi-squared random variable with m degrees of freedom divided by m.
. To find
2) Assume that Y is normally distributed
, where
and
,
you need to calculate
A)
.
C)
B)
.
.
D)
.
3) The covariance inequality states that
A)
.
B)
.
C)
.
D)
.
4) The expected value of a discrete random variable
A) equals the population median.
B) is computed as a weighted average of the possible outcome of that random variable, where the
weights are the probabilities of that outcome.
C) is the outcome that is most likely to occur.
D) can be found by determining the 50% value in the c.d.f.
5)
A)
.
C)
B)
.
.
D)
.
6) Let Y be a random variable. Then var(Y) equals
.
A)
7) The variance of
A)
.
B)
.
C)
.
D)
.
, is given by the following formula:
B)
.
C)
1
.
D)
.
8) The mean of the sample average
A)
.
B)
, is
C)
for n > 30.
.
D)
.
9) The central limit theorem
A) postulates that the sample mean
is a consistent estimator of the population mean
.
B) only holds in the presence of the law of large numbers.
C) states conditions under which a variable involving the sum of
i.i.d. variables becomes the
standard normal distribution.
D) states conditions under which a variable involving the sum of
i.i.d. variables becomes the
Student t distribution.
10) Two variables are uncorrelated in all of the cases below, with the exception of
A)
.
B) being independent.
C) having a zero covariance.
.
D)
11) The following types of statistical inference are used throughout econometrics, with the exception of
A) calibration.
B) estimation.
C) hypothesis testing.
D) confidence intervals.
12) The sample covariance can be calculated in any of the following ways, with the exception of:
, where
is the correlation coefficient.
A)
B)
.
C)
.
D)
.
13) When you are testing a hypothesis against a two-sided alternative, then the alternative is written as
A)
.
B)
14) To derive the least squares estimator
A)
.
B)
.
C)
.
D)
.
D)
.
, you find the estimator m which minimizes
.
C)
15) An estimator is
A) a nonrandom number.
B) an estimate.
C) a random variable.
D) a formula that gives an efficient guess of the true population value.
2
.
16) The probability of an event A or B (Pr(A or B)) to occur equals
A) Pr(A) + Pr(B) if A and B are mutually exclusive.
B) Pr(A) ˛ Pr(B).
Pr(A)
C)
.
Pr(B)
D) Pr(A) + Pr(B) even if A and B are not mutually exclusive.
can be defined as follows, with the exception of
17) Consistency for the sample average
A)
is consistent for
B)
.
.
C) the probability of
being in the range
becomes arbitrarily close to one as n increases for any
constant c > 0.
D)
has the smallest variance of all estimators.
is given by the following formula:
18) The standard error of
A)
.
B)
.
C)
.
D)
.
19) In econometrics, we typically do not rely on exact or finite sample distributions because
A) the covariances of
are typically not zero.
B) asymptotic distributions can be counted on to provide good approximations to the exact sampling
distribution.
C) variables typically are normally distributed.
D) we have approximately an infinite number of observations (think of re-sampling).
20) An estimator
A) E(
) > E(
of the population value
is more efficient when compared to another estimator
).
B) both estimators are unbiased, and var(
) < var(
C) it has a smaller variance.
D) its c.d.f. is flatter than that of the other estimator.
3
).
, if
Answer Key
Testname: PS2MC.TST
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Be
sure to write your answers in the table provided above
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
12)
13)
14)
15)
16)
17)
18)
19)
20)
D
D
C
B
B
B
A
A
C
D
A
C
C
C
C
A
D
C
B
B
1