Prof. Bryan Caplan

http://www.gmu.edu/departments/economics/bcaplan

Econ 345

Fall, 1998

Econometrics Pre-Test

This class requires competence in elementary mathematical statistics. You should definitely take the following pre-test to make sure that this is the right class for you. Answers for self-evaluation will be available next class.

Feel free to use books and calculators when taking the test, but spend no more than 90 minutes working on it.

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.

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.

3. A random variable generated by *doubling* a single roll of a normal six-sided die.

4. A random variable generated by *summing* two *separate* rolls of a normal six-sided die.

Evaluate the following expressions:

1.

2.

3.

4.

Determine the Probability of the Following Events:

*X* and *Y* are two normal six-sided dice.

1. P(*X-Y*=0)

2. P(*XY*=40)

3. P(*X*^{2}=*X+Y*)

4. P(*X+Y*<13)

*X* is a normal six-sided die; *Y* is a die with four sides numbered {1,2,3,4}.

1. P(*X*<5|*X+Y*=8)

2. P(*X+Y>*4|*X<5*)

3. P(*XY*<10|*X+Y*<8)

4. P(*X*/Y=1|X<5)

Take the Derivative of F(*x*):

1. F(*x*)=

2. F(*x*)=

3. F(*x*)=

4. F(*x*)=