ENGR361

# ENGR361 - number when the random sample is considered as a...

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Steven Weber Dept. of ECE Drexel University ENGR 361: Statistical Analysis of Engineering Systems (Fall, 2007) Quiz 8 Solutions (Wednesday, November 14) Question 1. Draw the empirical distribution, ˆ F ( z ) , for the three data points: x 1 = - 2 , x 2 = 1 , x 3 = 4 . z - 2 1 4 1 / 3 2 / 3 ˆ F ( z ) Question 2. Deﬁne a statistic. Name the two statistics introduced in class. When is a statistic a random variable and when is a statistic a number? A statistic is a function of the data. The two statistics introduced in class were the sample mean, ¯ X = ( X 1 + · · · + X n ) /n , and the sample variance, S 2 = 1 n - 1 n i =1 ( X i - ¯ X ) 2 . A statistic is a random variable when the random sample is considered as a sequence of random variables (before the experiment is run). A statistic is a
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Unformatted text preview: number when the random sample is considered as a sequence of numbers (after the experiment is run). Question 3. Write in words what is meant by the following four expressions: • E [ ¯ X ]: the expected value of the sample mean. • Var( ¯ X ): the variance of the sample mean. • E [ S 2 ]: the expected value of the sample variance. • Var( S 2 ): the variance of the sample variance. www.ece.drexel.edu/faculty/sweber 1 November 14, 2007...
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## This note was uploaded on 04/05/2010 for the course ENGR 361 taught by Professor Eisenstein during the Spring '04 term at Drexel.

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