estexamples

estexamples - Estimation More Examples Example 1 Let X 1 ;X...

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

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Estimation More Examples Example 1 Let X 1 ;X 2 ;:::;X n be a random sample from the Poisson distribution with mean . a. Find a point estimator for using the rst moment with the method of moments technique. Solution The rst moment is: E ( X ) = : By equating this to the rst theoretical moment and solving for , we see that: ^ = P n i =1 x i n : b. Find the maximum likelihood estimator for . Solution The log-likelihood is: l ( ) = n X i =1 ( x i ln( ) ln( x !)) n: The rst derivative is: dl ( ) d = n X i =1 x i ! n: Solving dl ( ) d = 0 for , we see that the maximum likelihood estimator is: ^ = P n i =1 x i n : Example 2 A random sample of n bike helmets manufactured by a certain company is selected. Let X be the number among the n that are awed and let p be the probability that a randomly selected helmet is awed. Assume that only X is observed (not the sequences of successes and failures)....
View Full Document

Page1 / 2

estexamples - Estimation More Examples Example 1 Let X 1 ;X...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online