Prof. Bryan Caplan
bcaplan@gmu.eduhttp://www3.gmu.edu/departments/economics/bcaplan
Econ 345
Fall, 1998
Econometrics Pre-Test Answers
Here are the answers for the Pre-Test. If you got less than 50% of the questions correct, you should consider dropping, because you will probably have to work very hard to get a decent grade in the class. If you got between 50-75% of the answers right, you will still find the class doable so long as you spend plenty of time on it. If you got 75-100% of the questions right, you will probably be well-prepared for this class. If you got over 75% of the questions right, and have an interest in going to graduate school, please talk to me after class or e-mail me. The graduate econometrics class I will be teaching next semester may be a better choice for you.
Find E(X), E(X2), Var(X), and SD(X), where X is:
1. A random variable generated by rolling a normal six-sided die.
E(X)=3.5 E(X2)=15.167 Var(X)=2.917 SD(X)=1.708
2. A random variable that is equal to 0 25% of the time, 1 50% of the time, 2 20% of the time, and 10 5% of the time.
E(X)=1.4 E(X2)=6.3 Var(X)=4.34 SD(X)=2.083
3. A random variable generated by doubling a single roll of a normal six-sided die.
E(X)=7 E(X2)=60.667 Var(X)=11.667 SD(X)=3.416
4. A random variable generated by summing two separate rolls of a normal six-sided die.
E(X)=7 E(X2)=54.833 Var(X)=5.833 SD(X)=2.415
Evaluate the following expressions:
1.
2. 
3. 
4. 
Determine the Probability of the Following Events:
1. P(X-Y=0)=1/6
2. P(XY=40)=0
3. P(X2=X+Y)=2/36
4. P(X+Y<13)=1
1. P(X<5|X+Y=8)=1/3
2. P(X+Y>4|X<5)=.625
3. P(XY<10|X+Y<8)=13/18
4. P(X/Y=1|X<5)=1/4
Take the Derivative of F(x):
1. F(x)=
; F'(x)=
2. F(x)=
; F'(x)=
3. F(x)=
; F'(x)=
4. F(x)=
; F'(x)=0