Prof. Bryan Caplan

http://www.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(X^{2}), 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(X^{2})=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(X^{2})=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(X^{2})=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(X^{2})=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(*X*^{2}=*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