Question 1

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 2

var(aX + bY)=

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 3

What would the correlation coefficient be if all observations for the two variables were on a curve described by Y = X2?

Accepted Answer

The correlation coef

Question 4

Two random variables X and Y are independently distributed if all of the following conditions hold,with the exception of

Accepted Answer

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   )]. 
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   )].

Question 5

The variance of   ,is given by the following formula:

Accepted Answer

A)    . 
B)    . 
C)    . 
D)    . 
A)    . 
B)    . 
C)    . 
D)    .

Question 6

Assume that you assign the following subjective probabilities for your final grade in your econometrics course (the standard GPA scale of 4 = A to 0 = F applies):   The expected value is:

Accepted Answer

A) 3.0 
B) 3.5 
C) 2.78 
D) 3.25 
A) 3.0 
B) 3.5 
C) 2.78 
D) 3.25

Question 7

Looking at a large CPS data set with over 60,000 observations for the United States and the year 2004,you find that the average number of years of education is approximately 13.6.However,a surprising large number of individuals (approximately 800)have quite a low value for this variable,namely 6 years or less.You decide to drop these observations,since none of your relatives or friends have that few years of education.In addition,you are concerned that if these individuals cannot report the years of education correctly,then the observations on other variables,such as average hourly earnings,can also not be trusted.As a matter of fact you have found several of these to be below minimum wages in your state.Discuss if dropping the observations is reasonable.

Accepted Answer

While it is always a good idea to check

Question 8

Probabilities and relative frequencies are related in that the probability of an outcome is the proportion of the time that the outcome occurs in the long run.Hence concepts of joint,marginal,and conditional probability distributions stem from related concepts of frequency distributions.
You are interested in investigating the relationship between the age of heads of households and weekly earnings of households.The accompanying data gives the number of occurrences grouped by age and income.You collect data from 1,744 individuals and think of these individuals as a population that you want to describe,rather than a sample from which you want to infer behavior of a larger population.After sorting the data,you generate the accompanying table:
Joint Absolute Frequencies of Age and Income,1,744 Households
Age of head of household
X1 X2 X3 X4 X5   The median of the income group of $800 and above is $1,050.
(a)Calculate the joint relative frequencies and the marginal relative frequencies.Interpret one of each of these.Sketch the cumulative income distribution.
(b)Calculate the conditional relative income frequencies for the two age categories 16-under 20,and 45-under 65.Calculate the mean household income for both age categories.
(c)If household income and age of head of household were independently distributed,what would you expect these two conditional relative income distributions to look like? Are they similar here?
(d)Your textbook has given you a primary definition of independence that does not involve conditional relative frequency distributions.What is that definition? Do you think that age and income are independent here,using this definition?

Accepted Answer

(a)The joint relative frequencies and ma

Question 9

For a normal distribution,the skewness and kurtosis measures are as follows:

Accepted Answer

A) 1.96 and 4 
B) 0 and 0 
C) 0 and 3 
D) 1 and 2 
A) 1.96 and 4 
B) 0 and 0 
C) 0 and 3 
D) 1 and 2

Question 10

Using the fact that the standardized variable Z is a linear transformation of the normally distributed random variable Y,derive the expected value and variance of Z.

Accepted Answer

Z = @#IMG-DLM& Y = a + bY,with

Question 11

Math and verbal SAT scores are each distributed normally with N (500,10000).
(a)What fraction of students scores above 750? Above 600? Between 420 and 530? Below 480? Above 530?
(b)If the math and verbal scores were independently distributed,which is not the case,then what would be the distribution of the overall SAT score? Find its mean and variance.
(c)Next,assume that the correlation coefficient between the math and verbal scores is 0.75.Find the mean and variance of the resulting distribution.
(d)Finally,assume that you had chosen 25 students at random who had taken the SAT exam.Derive the distribution for their average math SAT score.What is the probability that this average is above 530? Why is this so much smaller than your answer in (a)?

Accepted Answer

(a)Pr(Y>750)= 0.0062;Pr(Y>600)= 0.

Question 12

The Student t distribution is

Accepted Answer

A) the distribution of the sum of m squared independent standard normal random variables. 
B) the distribution of a random variable with a chi-squared distribution with m degrees of freedom,divided by m. 
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. 
A) the distribution of the sum of m squared independent standard normal random variables. 
B) the distribution of a random variable with a chi-squared distribution with m degrees of freedom,divided by m. 
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.

Question 13

If variables with a multivariate normal distribution have covariances that equal zero,then

Accepted Answer

A) the correlation will most often be zero,but does not have to be. 
B) the variables are independent. 
C) you should use the χ2 distribution to calculate probabilities. 
D) the marginal distribution of each of the variables is no longer normal. 
A) the correlation will most often be zero,but does not have to be. 
B) the variables are independent. 
C) you should use the χ2 distribution to calculate probabilities. 
D) the marginal distribution of each of the variables is no longer normal.

Question 14

The central limit theorem

Accepted Answer

A) states conditions under which a variable involving the sum of Y1,... ,Yn i.i.d.variables becomes the standard normal distribution. 
B) postulates that the sample mean   is a consistent estimator of the population mean
  . 
C) only holds in the presence of the law of large numbers. 
D) states conditions under which a variable involving the sum of Y1,... ,Yn i.i.d.variables becomes the Student t distribution. 
A) states conditions under which a variable involving the sum of Y1,... ,Yn i.i.d.variables becomes the standard normal distribution. 
B) postulates that the sample mean   is a consistent estimator of the population mean
  . 
C) only holds in the presence of the law of large numbers. 
D) states conditions under which a variable involving the sum of Y1,... ,Yn i.i.d.variables becomes the Student t distribution.

Question 15

The height of male students at your college/university is normally distributed with a mean of 70 inches and a standard deviation of 3.5 inches.If you had a list of telephone numbers for male students for the purpose of conducting a survey,what would be the probability of randomly calling one of these students whose height is
(a)taller than 6'0"?
(b)between 5'3" and 6'5"?
(c)shorter than 5'7",the mean height of female students?
(d)shorter than 5'0"?
(e)taller than Shaquille O'Neal,the center of the Boston Celtics,who is 7'1" tall?
Compare this to the probability of a woman being pregnant for 10 months (300 days),where days of pregnancy is normally distributed with a mean of 266 days and a standard deviation of 16 days.

Accepted Answer

(a)Pr(Z > 0.5714)= 0.2839;
(b)Pr( -2 < Z

Question 16

Show in a scatterplot what the relationship between two variables X and Y would look like if there was
(a)a strong negative correlation.
(b)a strong positive correlation.
(c)no correlation.

Accepted Answer

The answer of Show in a scatterplot what the relationship...

Question 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

Accepted Answer

A) 0.67 
B) 0.05 
C) 0.95 
D) 0.33 
A) 0.67 
B) 0.05 
C) 0.95 
D) 0.33

Question 18

The probability of an outcome

Accepted Answer

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. 
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.

Question 19

The accompanying table shows the joint distribution between the change of the unemployment rate in an election year and the share of the candidate of the incumbent party since 1928.You think of this data as a population which you want to describe,rather than a sample from which you want to infer behavior of a larger population.
Joint Distribution of Unemployment Rate Change and Incumbent Party's Vote
Share in Total Vote Cast for the Two Major-Party Candidates,
1928-2000
   (a)Compute and interpret E(Y)and E(X).
(b)Calculate E(Y   = 1)and E(Y   = 0).Did you expect these to be very different?
(c)What is the probability that the unemployment rate decreases in an election year?
(d)Conditional on the unemployment rate decreasing,what is the probability that an incumbent will lose the election?
(e)What would the joint distribution look like under independence?

Accepted Answer

(a)E(Y)= 0.368;E(X)= 0.736.The probabili

Question 20

The central limit theorem states that

Accepted Answer

A) the sampling distribution of   is approximately normal. 
B)    . 
C) the probability that   is in the range
  ± c becomes arbitrarily close to one as n increases for any constant c > 0. 
D) the t distribution converges to the F distribution for approximately n > 30. 
A) the sampling distribution of   is approximately normal. 
B)    . 
C) the probability that   is in the range
  ± c becomes arbitrarily close to one as n increases for any constant c > 0. 
D) the t distribution converges to the F distribution for approximately n > 30.

var(aX + bY)=

What would the correlation coefficient be if all observations for the two variables were on a curve described by Y = X2?

Two random variables X and Y are independently distributed if all of the following conditions hold,with the exception of

The variance of ,is given by the following formula:

Assume that you assign the following subjective probabilities for your final grade in your econometrics course (the standard GPA scale of 4 = A to 0 = F applies): The expected value is:

For a normal distribution,the skewness and kurtosis measures are as follows:

Using the fact that the standardized variable Z is a linear transformation of the normally distributed random variable Y,derive the expected value and variance of Z.

The Student t distribution is

If variables with a multivariate normal distribution have covariances that equal zero,then

The central limit theorem

Show in a scatterplot what the relationship between two variables X and Y would look like if there was (a)a strong negative correlation. (b)a strong positive correlation. (c)no correlation.

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

The probability of an outcome

The central limit theorem states that

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Regression With a Single Regressor: Hypothesis Tests and Confidence Intervals

Linear Regression With Multiple Regressors

Hypothesis Tests and Confidence Intervals in Multiple Regression

Nonlinear Regression Functions

Assessing Studies Based on Multiple Regression

Regression With Panel Data

Regression With a Binary Dependent Variable

Instrumental Variables Regression

Experiments and Quasi-Experiments

Introduction to Time Series Regression and Forecasting

Estimation of Dynamic Causal Effects

Additional Topics in Time Series Regression

The Theory of Linear Regression With One Regressor

The Theory of Multiple Regression

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Exam 2: Review of Probability

var(aX + bY)=

What would the correlation coefficient be if all observations for the two variables were on a curve described by Y = X2?

Two random variables X and Y are independently distributed if all of the following conditions hold,with the exception of

The variance of ,is given by the following formula:

Assume that you assign the following subjective probabilities for your final grade in your econometrics course (the standard GPA scale of 4 = A to 0 = F applies): The expected value is:

For a normal distribution,the skewness and kurtosis measures are as follows:

Using the fact that the standardized variable Z is a linear transformation of the normally distributed random variable Y,derive the expected value and variance of Z.

The Student t distribution is

If variables with a multivariate normal distribution have covariances that equal zero,then

The central limit theorem

Show in a scatterplot what the relationship between two variables X and Y would look like if there was (a)a strong negative correlation. (b)a strong positive correlation. (c)no correlation.

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

The probability of an outcome

The central limit theorem states that

Economic Questions and Data

Review of Statistics

Linear Regression With One Regressor

Regression With a Single Regressor: Hypothesis Tests and Confidence Intervals

Linear Regression With Multiple Regressors

Hypothesis Tests and Confidence Intervals in Multiple Regression

Nonlinear Regression Functions

Assessing Studies Based on Multiple Regression

Regression With Panel Data

Regression With a Binary Dependent Variable

Instrumental Variables Regression

Experiments and Quasi-Experiments

Introduction to Time Series Regression and Forecasting

Estimation of Dynamic Causal Effects

Additional Topics in Time Series Regression

The Theory of Linear Regression With One Regressor

The Theory of Multiple Regression

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