Question 1

The conditional expectation of Y given X,E(Y   ,is calculated as follows:

Accepted Answer

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

Question 2

The sample average is a random variable and

Accepted Answer

A) is a single number and as a result cannot have a distribution. 
B) has a probability distribution called its sampling distribution. 
C) has a probability distribution called the standard normal distribution. 
D) has a probability distribution that is the same as for the Y1,... ,Yn i.i.d.variables. 
A) is a single number and as a result cannot have a distribution. 
B) has a probability distribution called its sampling distribution. 
C) has a probability distribution called the standard normal distribution. 
D) has a probability distribution that is the same as for the Y1,... ,Yn i.i.d.variables.

Question 3

What is the probability of the following outcomes?
(a)Pr(M = 7)
(b)Pr(M = 2 or M = 10)
(c)Pr(M = 4 or M ≠ 4)
(d)Pr(M = 6 and M = 9)
(e)Pr(M  10)

Accepted Answer

(a)0.167 or @#IMG-DLM& = @#IMG-DLM& ;
(b

Question 4

The kurtosis of a distribution is defined as follows:

Accepted Answer

A)    
B)    
C)    
D) E[(Y -   )4) 
A)    
B)    
C)    
D) E[(Y -   )4)

Question 5

Calculate the following probabilities using the standard normal distribution.Sketch the probability distribution in each case,shading in the area of the calculated probability.
(a)Pr(Z  1.96)
(d)Pr(Z  1.645)
(f)Pr(Z > -1.645)
(g)Pr(-1.96  z)= 0.10;find z.
(j. )Pr(Z  z)= 0.05;find z.

Accepted Answer

(a)0.5000;
(b)0.8413;
(c)0.025

Question 6

The accompanying table gives the outcomes and probability distribution of the number of times a student checks her e-mail daily:
Probability of Checking E-Mail
   Sketch the probability distribution.Next,calculate the c.d.f.for the above table.What is the probability of her checking her e-mail between 1 and 3 times a day? Of checking it more than 3 times a day?

Accepted Answer

@#IMG-DLM& Pr(1 ≤ Y

Question 7

In econometrics,we typically do not rely on exact or finite sample distributions because

Accepted Answer

A) we have approximately an infinite number of observations (think of re-sampling). 
B) variables typically are normally distributed. 
C) the covariances of Yi,Yj are typically not zero. 
D) asymptotic distributions can be counted on to provide good approximations to the exact sampling distribution (given the number of observations available in most cases). 
A) we have approximately an infinite number of observations (think of re-sampling). 
B) variables typically are normally distributed. 
C) the covariances of Yi,Yj are typically not zero. 
D) asymptotic distributions can be counted on to provide good approximations to the exact sampling distribution (given the number of observations available in most cases).

Question 8

The mean of the sample average   ,   ,is

Accepted Answer

A)    . 
B)    . 
C)    . 
D)    for n > 30. 
A)    . 
B)    . 
C)    . 
D)    for n > 30.

Question 9

The skewness of the distribution of a random variable Y is defined as follows:

Accepted Answer

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

Question 10

Let Y be a random variable.Then var(Y)equals

Accepted Answer

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

Question 11

To infer the political tendencies of the students at your college/university,you sample 150 of them.Only one of the following is a simple random sample: You

Accepted Answer

A) make sure that the proportion of minorities are the same in your sample as in the entire student body. 
B) call every fiftieth person in the student directory at 9 a.m.If the person does not answer the phone,you pick the next name listed,and so on. 
C) go to the main dining hall on campus and interview students randomly there. 
D) have your statistical package generate 150 random numbers in the range from 1 to the total number of students in your academic institution,and then choose the corresponding names in the student telephone directory. 
A) make sure that the proportion of minorities are the same in your sample as in the entire student body. 
B) call every fiftieth person in the student directory at 9 a.m.If the person does not answer the phone,you pick the next name listed,and so on. 
C) go to the main dining hall on campus and interview students randomly there. 
D) have your statistical package generate 150 random numbers in the range from 1 to the total number of students in your academic institution,and then choose the corresponding names in the student telephone directory.

Question 12

Use a standard spreadsheet program,such as Excel,to find the following probabilities from various distributions analyzed in the current chapter:
a.If Y is distributed N (1,4),find Pr(Y ≤ 3)
b.If Y is distributed N (3,9),find Pr(Y > 0)
c.If Y is distributed N (50,25),find Pr(40 ≤ Y ≤ 52)
d.If Y is distributed N (5,2),find Pr(6 ≤ Y ≤ 8)

Accepted Answer

The answers here are given together with

Question 13

Assume that Y is normally distributed N(μ,σ2).To find Pr(c1 ≤ Y ≤ c2),where c1 < c2 and di =   ,you need to calculate Pr(d1 ≤ Z ≤ d2)=

Accepted Answer

A) Φ(d2)- Φ(d1) 
B) Φ(1.96)- Φ(1.96) 
C) Φ(d2)- (1 - Φ(d1)) 
D) 1 - (Φ(d2)- Φ(d1)) 
A) Φ(d2)- Φ(d1) 
B) Φ(1.96)- Φ(1.96) 
C) Φ(d2)- (1 - Φ(d1)) 
D) 1 - (Φ(d2)- Φ(d1))

Question 14

Following Alfred Nobel's will,there are five Nobel Prizes awarded each year.These are for outstanding achievements in Chemistry,Physics,Physiology or Medicine,Literature,and Peace.In 1968,the Bank of Sweden added a prize in Economic Sciences in memory of Alfred Nobel.You think of the data as describing a population,rather than a sample from which you want to infer behavior of a larger population.The accompanying table lists the joint probability distribution between recipients in economics and the other five prizes,and the citizenship of the recipients,based on the 1969-2001 period.
Joint Distribution of Nobel Prize Winners in Economics and Non-Economics Disciplines,and Citizenship,1969-2001
   (a)Compute E(Y)and interpret the resulting number.
(b)Calculate and interpret E(Y   =1)and E(Y   =0).
(c)A randomly selected Nobel Prize winner reports that he is a non-U.S.citizen.What is the probability that this genius has won the Economics Nobel Prize? A Nobel Prize in the other five disciplines?
(d)Show what the joint distribution would look like if the two categories were independent.

Accepted Answer

(a)E(Y)= 0.53.7 .53.7 percent of Nobel P

Question 15

The expected value of a discrete random variable

Accepted Answer

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. 
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.

Question 16

The table accompanying lists the joint distribution of unemployment in the United States in 2001 by demographic characteristics (race and gender).
Joint Distribution of Unemployment by Demographic Characteristics,
United States,2001
   (a)What is the percentage of unemployed white teenagers?
(b)Calculate the conditional distribution for the categories "white" and "black and other."
(c)Given your answer in the previous question,how do you reconcile this fact with the probability to be 60% of finding an unemployed adult white person,and only 22% for the category "black and other."

Accepted Answer

(a)Pr(Y = 0,X = 0)= 0.13.
(b)
Conditiona

Question 17

The covariance inequality states that

Accepted Answer

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

Question 18

Consistency for the sample average   can be defined as follows,with the exception of

Accepted Answer

A)    converges in probability to
  . 
B)    has the smallest variance of all estimators. 
C)    . 
D) the probability of   being in the range
  ± c becomes arbitrarily close to one as n increases for any constant c > 0. 
A)    converges in probability to
  . 
B)    has the smallest variance of all estimators. 
C)    . 
D) the probability of   being in the range
  ± c becomes arbitrarily close to one as n increases for any constant c > 0.

Question 19

SAT scores in Mathematics are normally distributed with a mean of 500 and a standard deviation of 100.The formula for the normal distribution is   .Use the scatter plot option in a standard spreadsheet program,such as Excel,to plot the Mathematics SAT distribution using this formula.Start by entering 300 as the first SAT score in the first column (the lowest score you can get in the mathematics section as long as you fill in your name correctly),and then increment the scores by 10 until you reach 800.In the second column,use the formula for the normal distribution and calculate f(Y).Then use the scatter plot option,where you eventually remove markers and substitute these with the solid line option.

Accepted Answer

The answer of SAT scores in Mathematics are normally distributed...

Question 20

To standardize a variable you

Accepted Answer

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. 
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.

The conditional expectation of Y given X,E(Y ,is calculated as follows:

The sample average is a random variable and

What is the probability of the following outcomes? (a)Pr(M = 7) (b)Pr(M = 2 or M = 10) (c)Pr(M = 4 or M ≠ 4) (d)Pr(M = 6 and M = 9) (e)Pr(M < 8) (f)Pr(M = 6 or M > 10)

The kurtosis of a distribution is defined as follows:

In econometrics,we typically do not rely on exact or finite sample distributions because

The mean of the sample average , ,is

The skewness of the distribution of a random variable Y is defined as follows:

Let Y be a random variable.Then var(Y)equals

To infer the political tendencies of the students at your college/university,you sample 150 of them.Only one of the following is a simple random sample: You

Assume that Y is normally distributed N(μ,σ2).To find Pr(c1 ≤ Y ≤ c2),where c1 < c2 and di = ,you need to calculate Pr(d1 ≤ Z ≤ d2)=

The expected value of a discrete random variable

The covariance inequality states that

Consistency for the sample average can be defined as follows,with the exception of

To standardize a variable you

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Review of Statistics

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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

The conditional expectation of Y given X,E(Y ,is calculated as follows:

The sample average is a random variable and

What is the probability of the following outcomes? (a)Pr(M = 7) (b)Pr(M = 2 or M = 10) (c)Pr(M = 4 or M ≠ 4) (d)Pr(M = 6 and M = 9) (e)Pr(M < 8) (f)Pr(M = 6 or M > 10)

The kurtosis of a distribution is defined as follows:

In econometrics,we typically do not rely on exact or finite sample distributions because

The mean of the sample average , ,is

The skewness of the distribution of a random variable Y is defined as follows:

Let Y be a random variable.Then var(Y)equals

To infer the political tendencies of the students at your college/university,you sample 150 of them.Only one of the following is a simple random sample: You

Assume that Y is normally distributed N(μ,σ2).To find Pr(c1 ≤ Y ≤ c2),where c1 < c2 and di = ,you need to calculate Pr(d1 ≤ Z ≤ d2)=

The expected value of a discrete random variable

The covariance inequality states that

Consistency for the sample average can be defined as follows,with the exception of

To standardize a variable you

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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