Question

1. 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.

2. 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.

3. 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).

4. 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.

a. Find the expected GPA when SAT = 700, that is, find E(GPA|SAT=700).

Answer 1