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mid01_sample_sol

# mid01_sample_sol - ISyE 2028A Summer 2010 1 Let X 1 X n be...

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ISyE 2028A, Summer 2010 Friday June 4 Midterm 1 (Sample) Solutions 1. Let 1 ,, n XX  be a random sample from a probability mass function or probability density function f ( x ). For k = 1,2,3,……, the k th population moment is denoted by __________, while the k th sample moment is __________. ANSWER: 1 ( ), (1/ ) n kk i i EX n X = 2. If Z is a standard normal random variable, then ( 2.0) PZ ≤− = __________. ANSWER: .0228 3. Which of the following statements are correct if 2 1,2,. ...... ,? ii y xi n = ∀= A. 2 yx = B. 4 = C. 22 2 ss = D. 4 = + ANSWER: A 4. If the population distribution of a variable is approximately normal, then according to the empirical rule, which of the following statement is the most appropriate? A. Roughly 68% of the values are within one standard deviation of the mean. B. Roughly 95% of the values are within two standard deviations of the mean. C. Roughly 99.7% of the values are within three standard deviations of the mean. D. All of the above statements are correct. ANSWER: D 5. Answer the following two questions: a. If a constant c is added to each i x in a sample, yielding i y = i x + c

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mid01_sample_sol - ISyE 2028A Summer 2010 1 Let X 1 X n be...

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