final+fall+2009+solutions - ECI 114 Fall 2009 Name Final...

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Unformatted text preview: ECI 114 Fall 2009 Name Final (100 points) Thursday, Dec. 10, 2009, 3:30-5:30 pm Show your work. Its not necessary to give a final numerical answer unless specifically asked, but you need to provide all the information necessary to compute the final answer. Please circle or otherwise highlight your answer. Turn in your crib sheet and your normal, t- and chi-squared tables with your exam. Put your name on the back of the last page. GOOD LUCK! 1. For each of the following statements, circle the letter T if it is true, and F if it is false. (2 * 8 =16 points) T F a. Suppose A and B are two events. If Pr (A B) = 0, then A B = False. For example, for a standard normal distribution, let A = {x : x 0} and B = {x : x 0}, then A B = {0}. Pr (A B) = Pr{x = 0} = 0, but A B T F b. In counting rules, a combination is a special case of a partition. True. See Exercise 12 on page Prb-12 of the notes. T F c. For a continuous random variable X, if its pdf f(x) is constant, then X is uniformly distributed. True T F d. The Central Limit Theorem states that the distribution of the sample mean X approaches the normal distribution with mean and variance 2 if the X i s (i = 1, 2, , N) are identically distributed with mean and variance 2 , as N becomes sufficiently large. False. Those X i s (i = 1, 2, , N) must be independently and identically distributed, and if so, the variance of the sample mean would be 2 /N. The variance would not be 2 in any case. T F e. Let 9 1 1 / 9 i i X = = and 8 2 1 / 8 i i X = = be two estimators for the population mean. 2 is a better estimator than 1 . False. 1 ( ) E = , 2 ( ) E = . Both 1 and 2 are unbiased. 1 1 ( 9 ) Var = 2 , 2 1 ( ) 8 Var = 2 . Since 1 has a smaller variance, it is a better estimator than 2 T F f. When is known, the width of a two-sided 99% confidence interval for the population mean is a constant. True. The width of the interval is 2 z /s X-bar , which is a known constant if is known. Final, ECI 114, FALL 2009 Page 1 T F g. The P-value is the probability of being wrong if we reject the null hypothesis in a statistical test. True. T F h. If X ~ N(, 5 2 ), Y ~ N(, 2 ), and they are independent, then 2 Y X- ~ N(0, 1). False. Since Var(X-Y) = Var(X) + Var(Y), X - Y ~ N(0, 6 2 ). 6 X Y - ~ N(0, 1) 2. (9 points) Place the number of the most appropriate item from the group below in the blank next to each item below. Note: some formulas may be used more than once while others may not be used at all. One question may have multiple correct answers; you only need to give one....
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This note was uploaded on 01/19/2012 for the course ECI 114 taught by Professor Mocktarian during the Fall '08 term at UC Davis.

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final+fall+2009+solutions - ECI 114 Fall 2009 Name Final...

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