## Exam 2

Use points as an indicator of time (Total Points: 80). Pace yourself. Show all your work. Don’t panic! Good luck!

### 1.(18 points) The Adams Corporation stores spare parts at two warehouses, one in Baltimore and one in Gary.    经济统计考试代写

The number of defective and acceptable spare parts at each warehouse is givenbelow:

If one of the spare parts kept by the firm chosen at random (i.e., if each spare part has a 1/500 chance of being chosen), D and A denote the events that the spare part is defective or acceptable, while B and G denote the events that it comes from Baltimore or Gary.

Calculate each of the following probabilities.    经济统计考试代写

a.P(D)

b.P(A∪B)

c.P(A ∩B)

d.P(B|A)

e.P(A|not G)

f.Is the event denoted by D statistically independent of the event denoted byG? Why or whynot?

### 2.(8 points) An automobile manufacturer buys door handles from a supplier.

When each shipmentofdoor handles arrives, the automobile manufacturer takes a random sample of 10 door handles from the shipment of 10,000. If one or more door handle in the sample is defective, the automobile manufacturer rejects the shipment.

a.If 10 percent of the door handles in a shipment are defective, what is theprobability that the shipment will be rejected?

b.What is the expected number of defective door handles in a sample of10?

### 3.(6 points) Assume incomes in a population are approximately normally distributed with mean \$15,000 and standard deviation \$5,000.    经济统计考试代写

The poverty level of income is\$8,000.

a.What is the poverty rate?

b.What income is the 90thpercentile?

### 4.(9 points) In a particular factory, a motor generates power to be used intermittently by five workers.

Let X be the number of workers drawing power at any one time.

a.If more than two workers require power at the same time, the motor will notfunction properly. What is the probability of such a malfunction at any given moment?

b.What is the expected number of workers requiring power at any given point in time?

c.What is the standard deviation of the number of workers requiring power atany given point in time?

### 5.(12 points) For a particular life insurance policy, the lifetime of the policy holders follow a normal distribution with µ = 70 years and σ = 5.

This policy pays the first payment at age 65 and a payment every five years thereafter.

a.What percentage of policy holders will receive at least onepayment?    经济统计考试代写

b.What is the probability that the averagelength of life of a random sample of 9 policy holders will be over 75 years?

c.What does the sampling distribution of X , the average length of life of a sample of 9 look like? (i.e., what is the shape of the distribution, what is its mean and standard deviation?)

d.What do we mean when we say X is an unbiased estimate of µ?

### 6.(9 points ) Suppose two stocks W and Z are perfectly negatively correlated.    经济统计考试代写

W has an expected return of 10 and variance of 9; Z has an expected return of 4 and variance of 1.

a.If a person holds a portfolio with half of her wealth in each stock, find the expected return and variance for the portfolio. That is, find the mean and variance of Ywhere Y = q W + (1-q) Z and q=1/2.

b.For these two specific stocks there is a value of q that results in a risk free (zero variance) portfolio, which is, of course, the smallest variancethat any portfolio can achieve. Find that value of q.

### 7.(18 points) I am interested in studying how minutes of leisure differ by gender and by whether someone has young children.

Using data from the American Time Use Survey 2010 which collects 24 hour time diaries from a large number of Americans, I ran the following Stata commands. The variableyk017 is a dummy variable which takes on a 1 if the person’s youngest child is between the ages of 0 and 17. Below are the commands I typed into Stata:

gen Agesq=Age*Age

gen female=1 if sex==2 replace female=0 if sex==1

gen married_wkids=0

replace married_wkids=1 if married==1 & yk017==1

gen married_nokids=0

replace married_nokids=1 if married==1 & yk017==0

gen single_nokids=0

replace single_nokids=1 if married==0 & yk017==0

gen single_wkids=0

replace single_wkids=1 if married==0 & yk017==1

gen f_married_wkids=0

replace f_married_wkids=1 if married_wkids==1 & female==1 gen f_married_nokids=0

replace f_married_nokids=1 if married_nokids==1 & female==1 gen f_single_wkids=0

replace f_single_wkids=1 if single_wkids==1 & female==1 gen f_single_nokids=0

replace f_single_nokids=1 if single_nokids==1 & female==1

gen m_married_wkids=0

replace m_married_wkids=1 if married_wkids==1 & female==0 gen m_married_nokids=0

replace m_married_nokids=1 if married_nokids==1 & female==0 gen m_single_wkids=0

replace m_single_wkids=1 if single_wkids==1 & female==0 gen m_single_nokids=0

replace m_single_nokids=1 if single_nokids==1 & female==0

a.What is the difference between the following two regression commands? When would I use one versus the others? Be concrete in your answer.

Note that the /* and */ symbols just allow us to write a long command on multiple lines instead of it extending off the screen.    经济统计考试代写

regress minutes_leisure female married_wkids married_nokids single_wkids /*

*/ Educ Age Agesq Friday saturday Sunday

regress minutes_leisure f_married_wkids f_married_nokids f_single_wkids /*

*/f_single_nokids m_married_wkids m_married_nokids m_single_wkids /*

*/ Educ Age Agesq Friday saturday Sunday

b.The variable diarydayis the day of the week the time diary was collected. In diaryday, Sunday is coded as 1, Monday is coded as 2, etc. Please write the Stata code to generate three dummy variables, Friday, saturday and Sunday.

#### c.Here is the Stata regression command I ran and the exact results I received.

Which household status/gender group in the sample has the most leisure minutes? How many leisure minutes do they have on Sundays?  经济统计考试代写

d.Basedon my Stata output, which household status group in this sample has the biggest gender gap in leisure minutes?

e.Please comment on the effect of age on minutes of leisure time in this sample.