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# ProblemSet1 Answers - Professor Mumford [email protected]

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Professor Mumford Econ 360 - Fall 2010 Problem Set 1 Answers True/False (20 points) 1. TRUE If { a 1 ,a 2 ,...,a n } are constants and { X 1 ,X 2 ,...,X n } are random variables then: E n X i =1 a i X i ! = n X i =1 a i E ( X i ) 2. FALSE For a random variable X , let μ = E ( X ). The variance of X can be expressed as: V ar ( X ) = E ( X 2 ) - μ 2 3. TRUE An estimator, W , of θ is an unbiased estimator if E ( W ) = θ for all possible values of θ . 4. FALSE The central limit theorem states that the average from a random sample for any population (with ﬁnite variance) when it is standardized, by subtracting the mean and then dividing by the standard deviation, has an asymptotic standard normal distribution. 5. FALSE Inferring causality is sometimes possible without a designed experiment. Using observational data to infer causality is what econometrics is all about. 1

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Multiple Choice Questions (20 points) 6. The idea of holding “all else equal” is known as (a) ceteris paribus (b) correlation (c) causal eﬀect (d) independence 7. If our dataset has one observation for every state for the year 2000, then our dataset is (a) cross-sectional data (b) pooled cross-sectional data
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ProblemSet1 Answers - Professor Mumford [email protected]

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