Temple University

Department of Economics

Economics 615

Econometrics I

Midterm Exam

Directions: This is a closed book exam. You may have 2 1/2 hours to complete the exam. You must answer all questions. The point values are shown. Your answers must be your own work.

  1. (25 points) Use the following joint distribution
 

X

  

0

1

2

3

  

Y

1

1/8

0

0

1/8

1/4

2

0

1/4

1/4

0

1/2

3

0

1/8

1/8

0

1/4
   

1/8

3/8

3/8

1/8

1
  1. What is E(X)?
  2. What is E(Y)?
  3. What is E(X|Y=2)?
  4. What is E(X|Y=1)?
  5. What is E(XY)?
  6. What is the covariance of X and Y?
  7. Are X and Y independent? How do you know? How do you reconcile your answers in a., c., d., and f.?

2. (20 points) For the probability density

  1. Is this a bona fide density? How do you know?
  2. Find E(X).
  3. Find Variance(X).

3. (10 points) If x has a normal distribution with mean 3 and variance 16, what are the following:

  1. Prob[ |x| > 7 ] ?
  2. Prob[ x > -2 | x<4 ] ?

4. (30 points) For the sample data 12, 15, 9, 3, 23, 1, 5, 8, 11, 17 drawn from a normal distribution with mean and variance.

  1. Compute the sample mean.
  2. Compute the sample standard deviation.
  3. Test the hypothesis

    4. at the 95% level using the classical framework.

  4. Test the hypothesis

    5. at the 95% level using the classical framework.

  5. Using a likelihood ratio test, test the following hypothesis:

at the 95% level.

5. (15 points) Suppose that in a sample of 100 observations from a normal distribution with mean and variance you are told that 25% of the observations are less than 2.5 and 55% are less than 5.3. Estimate and .