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Unformatted text preview: Northwestern University Department of Economics - STAT 210 Introduction to Statistics Professor: Steffen Habermalz - Second Midterm Examination February 20 th 2009 INSTRUCTIONS : Read the whole exam first. Questions are not ordered by difficulty. Answer all questions. Make sure you show ALL your work in order to receive full credit. Write legibly. 1. (2+3=5 pts. each) True/False: State if the following statements are true or false. Only clearly explained answers earn full credit. a. If X~N(5,81) then ( 29 ( 29 5 5 P X P X < = . TRUE. Since the normal distribution is continuous. b. The 2-sided 4% critical value of the standard normal distribution is 2.5 FALSE. They are -2.05 and 2.05. c. No linear estimator has a lower variance than the sample mean. FALSE. The sample mean is BLUE, it is the best linear UNBIASED estimator. d. A biased estimator cannot be consistent. FALSE. We showed in class that 2 2 1 1 ( ) N X i i s X X N = =- % is biased but consistent. e. 2 1 N i i X N X = FALSE. We know that since the sample variance is always nonnegative, then = - N i i X N X 1 2 2 , but that does no imply = - N i i X N X 1 2 . For example, consider N=2 and 5 . 1 = X , 25 . 2 = X . Then 2 2 2 1 3125 . 75 . 2 X X X + = = . 2. Consider random variable X which can take on values 0, 1 and 2 with the following probability distribution: P(X=0)=1/2, P(X=1)=1/4 and P(X=2)=1/4....
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- Winter '09