Economics and Statistics > QUESTIONS & ANSWERS > University Of Chicago_ECONOMICS 21020_Problem Set 1 Partial Solutions-ALL CORRECTED (All)

University Of Chicago_ECONOMICS 21020_Problem Set 1 Partial Solutions-ALL CORRECTED

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ECON 210: Problem Set 1 Statistics Review Due April 9th, 2018 at the beginning of class 1 (39 points) Stock and Watson, Exercises 3.2, 3.3, and 3.4 2 (6 points) Let X be a Bernoulli random varia ... ble (i.e. P (X = 1) = p and P (X = 0) = 1 − p). Define a new random variable Y = 10X2 + 5X. What are E(Y ) and V ar(Y )? Solution (it’s okay if not fully simplified): E(Y ) = E(10X2 + 5X) = p(10 + 5) + (1 − p) and V ar(Y ) = E(Y 2) − E(Y )2 = 152p + (1 − p) − (15p + (1 − p))2 3 (5 points) Let X and Y be random variables and a; b; c; d be constants. Show that Cov(aX + b; cY + d) = acCov(X; Y ) Solution: Full credit for writing the covariance in terms of expectations and doing the algebra 4 (10 points) Let X; Y; and be random variables with Y = 2X2 −4X + , E(X) = 2, V ar(X) = 6, E(X3) = 10, V ar() = 1 and E(jX) = 0. What are 1. E(Y jX = 2) 2. E(Y jX) 3. E(Y ) 4. V ar(Y − 2X2) 5. Cov(X; Y ) Solution (it’s okay if not fully simplified, but need to use LIE to get rid of any terms): 1. E(Y jX = 2) = 2 ∗ 22 − 4 ∗ 2 = 0 2. E(Y jX) = 2X2 − 4X [Show More]

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