Assignment 1 Econometrics-Conditional Expectation A random variable Y

Assignment #1
Econometrics
Due: Thursday September 14th at 9:30 AM 1
1.1 Theory
Conditional Expectation A random variable Y is equal to six plus three times a random variable X:
Y =6+3×X
What is:
E[Y |X = c] ? E[Y |X = c + 1] = ?? 1.2 Application to Finance You are trying to choose how to allocate a portfolio of $1,000. There are five potential
investments: A, B, C, D, and E. The following table gives the expected rate of return in
each investment and its standard deviation:
Investment
A
B
C
D
E Rate of Return
.05
.05
.05
.05
.05 Variance of Return
.06
.07
.08
.06
.035 A, B, C, and D each have a minimum investment of $500. E has a minimum investment of
$1,000. All of the investments are independent of one another, except for B and C which
have a covariance of ?.02. What is the risk-minimizing portfolio? What is its expected
return and the variance of its return? 1 1.3 Independence Given the following facts, determine which pairs of variables are independent:
E[X1 ] =7
E[X2 ] =9
E[X1 × X2 ] =E[Y1 |Y2 = 4]
Y1 =3 + 15 × Y2 1.4 Principles of Variance and Covariance Let A and B be two random variables. Further, let
V ar(A ? B) = V ar(A) + V ar(B) + 12
What is Cov(A, B)?
Let E[B] = 0, what is E[AB]? 2 R programming Import the data set CPS.csv. The data has hourly earnings, education level, gender, and
age for a large group of people surveyed by the Census in 2004. Let E by the hourly
earnings of a randomly chosen person from the survey, let A be that person’s age, D be
that person’s degree, and G be that person’s gender.
1. Find E[E]
2. Find E[A]
3. Find E[E|A = 30]
4. Find E[E|G = Female]
5. Find E[E|D = college]
6. Find E[E|D = high school] 2