Economic Problem Set

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

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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 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 ...

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