prob1 - The University of Illinois at Chicago Economics 346...

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The University of Illinois at Chicago Economics 346: Econometrics Problem Set 1 Show your works for full credit. 1. Assuming there are only 50 stock portfolios in the world, and the rates of return (X i ) are following: Xi Xi+100 Xi*100 Frequency 0.05 100.05 5 2 0.06 100.06 6 3 0.07 100.07 7 8 0.08 100.08 8 11 0.09 100.09 9 7 0.10 100.10 10 9 0.11 100.11 11 6 0.12 100.12 12 4 a) What are the mean and median rates of return? b) What are the variance and standard deviation of the rates of return? c) Prove following properties of the mean using the data. E(X i +100) = 100 + E(X i ) E(X i *100) = 100* E(X i ) d) Prove following properties of the variance using the data. Var(X i *100) = 10000* Var(X i ) Var(X i +100) = Var(X i ) 2. From local real estate listing service, we got following price information. Answer the following questions using the table. House Price X 150000 175000 200000 250000 275000 300000 325000 350000 400000 Number of House 2 4 5 9 12 20 10 5 4 a) Find the probability of each house price. b) Assuming the data represents the whole population, find population mean (), population variance, and population standard deviation.

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