Recitation9Solutions

Recitation9Solutions - Steven Weber Dept of ECE Drexel...

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Steven Weber Dept. of ECE Drexel University ENGR 361: Statistical Analysis of Engineering Systems (Spring, 2008) Recitation 9 Solutions (Friday, May 30) Question 1. Suppose the population distribution is uniform over [ a, b ] : f X ( x ) = ± 1 b - a , a x b 0 , else . (1) Suppose the constants a, b are unknown, and hence we gather a random sample, X 1 , . . . , X n to determine them. Please do the following: Find the ML estimators for a, b . Hint: pay attention to the regime where the likelihood function is zero (equiv- alently, where the log-likelihood function is infinitely negative), and that monotonically increasing functions (derivative of constant sign) are maximized at a boundary point. In particular, form the function: L ( x 1 , . . . , x n ; a, b ) = log f ( x 1 , . . . , x n ; a, b ) = log n Y i =1 f ( x i ; a, b ) = n X i =1 log f ( x i ; a, b ) , (2) noting where f ( x i ; a, b ) = 0 , and thus where L ( x 1 , . . . , x n ; a, b ) = -∞ . From here, compute
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This note was uploaded on 06/24/2008 for the course ENGR 361 taught by Professor Eisenstein during the Spring '04 term at Drexel.

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Recitation9Solutions - Steven Weber Dept of ECE Drexel...

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