# HW1 - (2.c Using properties of the population mean and...

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Econ 444 Elementary Econometrics (Fall 2010) HOMEWORK EXERCISE: 1 Due in class on Thursday, Jan 21 or Friday, Jan 22 Depending on When We Meet for the Make-up Class Q1. Choose the one alternative that best completes the statement or an- swers the question. 1)An estimator ˆ μ of the population parameter μ is unbiased if A) E μ ) = μ . B)ˆ μ = μ . C) V ar μ ) = 0 . D)Sample is very big. 2)An estimator ˆ μ of the population parameter μ is more eﬃcient when com- pared to another estimator ˜ μ if A)Sample is representative of true population. B)Both estimators are unbiased, and V ar μ ) < V ar μ ). C)It has a smaller variance. D) E μ ) > E μ ). 2. Suppose the probability distribution for a random variable X i is given as : i X i P X i 1 2 1/12 2 4 1/4 3 6 5/12 4 8 1/6 5 10 1/12 (2.a) Plot the probability distribution. (2.b) Compute E(X) and Var(X).

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Unformatted text preview: (2.c) Using properties of the population mean and variance compute E(2+3X) and Var(3X) 1 3. Expand the following expressions : (3.a) ∑ 6 i =1 X i Y i (3.b) ∑ 4 i =1 X i Y i ∑ 4 i =1 X i ∑ 4 i =1 Y i 4. Imagine that you have data on the demand of the CD at the price levels of \$9, \$12, an \$16 for three CD stores on various days. Suppose that the data were as follows: Table 1 Observed Demand for a CD Observation Price The observed number of copies of the CD demanded i X i Y i (1) (2) (3) 1 9 21 2 12 16 3 16 4 (4.a) Compute the sample mean of X, ¯ X , and the sample mean of Y, ¯ Y . (4.b) Compute ∑ 3 i =1 ( X i-¯ X ) 2 (4.c) Compute ∑ 3 i =1 ( X i-¯ X )( Y i-¯ Y ) . 2...
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HW1 - (2.c Using properties of the population mean and...

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