Hw11 - SIEO 3600(IEOR Majors Assignment#11 Introduction to...

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Unformatted text preview: SIEO 3600 (IEOR Majors) Assignment #11 Introduction to Probability and Statistics April 15, 2010 Assignment #11 ( Maximum likelihood estimator and confidence interval ) 1. Let X 1 ,...,X n be a sample from the distribution whose density function is f X ( x ) = e- ( x- θ ) , x ≥ θ, , otherwise . Determine the maximum likelihood estimator of θ . Hint: You cannot match the derivative of log L ( θ ) to 0 in this case. 2. The PBC concentration of a fish caught in Lake Michigan was measured by a technique that is known to result in an error of measurement that is normally distributed with a standard deviation of .08 ppm (parts per million). Suppose the results of 20 independent measurements of this fish are 11 . 2 , 12 . 4 , 10 . 8 , 11 . 6 , 12 . 5 , 10 . 1 , 11 . , 12 . 2 , 12 . 4 , 10 . 6 , 9 . 7 , 13 . 4 , 10 . 3 , 8 . 9 , 11 . 5 , 9 . 9 , 10 . 1 , 9 . 3 , 12 . 6 , 11 . 3 Give a 95% confidence interval for the PBC level of this fish....
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