{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Recitation9Solutions

# Recitation9Solutions - Steven Weber Dept of ECE Drexel...

This preview shows pages 1–2. Sign up to view the full content.

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 i =1 f ( x i ; a, b ) = n 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 ∂a L ( x 1 , . . . , x n ; a, b ) and ∂b L ( x 1 , . . . , x n ; a, b ) , and identify the values a, b that maximize L ( x 1 , . . . , x n ; a, b ) .

This preview has intentionally blurred sections. Sign up to view the full version.

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

{[ snackBarMessage ]}