 Economic Problem Set

### Question Description

Question 6-8 required. Please provide a copy of hand-writing solution with full steps. Please show all steps.

### Unformatted Attachment Preview

Econ 122A Problem Set 1 Due in class on Jan 23 Name(Print)______________________ UCI ID_____________________________ 1. Assume Y=1+2X+u, where X, Y, and u=v+X are r.v.s, v is independent of X; E(v)=0, Var (v)=1 , E(X)=4, and Var(X)=2. 1) Calculate E(u|X), E(Y|X), E(u|X=1), E(Y|X=1), E(u) and E(Y). 2) Calculate Var(u|X), Var(Y|X), Var(u|X=1), Var(Y|X=1). 2. Assume Y=1+2X+u, where X, Y, and u=vX are r.v.’s, v is independent of X with E(v)=0, Var (v)=1 , E(X)=4 and Var(X)=2. 1) Calculate E(u|X), E(Y|X), E(u|X=1), E(Y|X=1) ), E(u) and E(Y). 2) Calculate Var(u|X), Var(Y|X), Var(u|X=1) and Var(Y|X=1). 3. Let Y denote the average starting salary for 2014 U.S. college graduates, measured in dollars. Suppose that the average annual salary is \$56,000 dollars, with a standard deviation of 8,000. Find the mean and standard deviation when salary is measured in thousands of dollars. 4. Let X denote daily work hours. Suppose that for the sample of workers you have, the average daily work hours are 8 hours, with a standard deviation of 5. Suppose now let Z denote weekly work hours, find the mean and standard deviation for Z (assuming everyone works 5 days per week in your sample). 1 5. Suppose that at a large university, college grade point average, GPA , and SAT score, SAT, are related by the conditional expectation E(GPA|SAT)=.8+.002SAT. 1) Find the expected GPA when SAT = 700, that is, find E(GPA|SAT=700). 2) If a student’s SAT score is 760, does this mean he or she will have the GPA found in part 1)? Why or Why not? 6. Suppose that you have a sample of 500 observations on two random variables: price denoted as X, and profit, denoted as Y. So you observe {xi, yi} for i=1,…500. Write down the formula for sample mean and sample variance of X and Y as well as the sample covariance between X and Y. 7. Which of the following distribution is not symmetric? A. F distribution, B. t distribution, C. Standard normal distribution, D. Normal distribution with mean 1 and standard deviation 1. 8. Show each of the following 2 n (1) 0 ∑ (x − x ) = i =1 i n (2)∑ x = nx i =1 n (3)∑ xi = nx i =1 n ∑ ( x − x )( y =i 1 (4) i n ∑ (x − x ) =i 1 n − y) ∑ x (y = n ∑ ( xi − x )( yi − y ) ∑ (x − x ) n ≠ ∑(y =i 1 =i 1 n n 2 i =i 1 =i 1 (5) n ∑ (x − x ) y − y) i i i =i 1 =i 1 n n 2 2 i i =i 1 =i 1 ∑ (x − x ) i = i i ∑ (x − x ) i − y) ∑ (x − x ) i 3 2 ... This question has not been answered.

Create a free account to get help with this and any other question! Brown University

1271 Tutors California Institute of Technology

2131 Tutors Carnegie Mellon University

982 Tutors Columbia University

1256 Tutors Dartmouth University

2113 Tutors Emory University

2279 Tutors Harvard University

599 Tutors Massachusetts Institute of Technology

2319 Tutors New York University

1645 Tutors Notre Dam University

1911 Tutors Oklahoma University

2122 Tutors Pennsylvania State University

932 Tutors Princeton University

1211 Tutors Stanford University

983 Tutors University of California

1282 Tutors Oxford University

123 Tutors Yale University

2325 Tutors