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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
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