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

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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....
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online