Isye 2027

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

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

Unformatted text preview: or each value of θ, then recall from the interpretation, (3.2), of a pdf, that for sufficiently small, fθ (u) ≈ 1 P u − 2 < X < u + 2 . That is, fθ (u) is proportional to the probability that the observation is in an -width interval centered at u, where the constant of proportionality, namely 1 , is the same for all θ. Following tradition, in this context, we call fθ (u) the likelihood of the observation u. The maximum likelihood estimate of θ for observation u, denoted by θM L (u), is defined to be the value of θ that maximizes the likelihood, fθ (u), with respect to θ. 98 CHAPTER 3. CONTINUOUS-TYPE RANDOM VARIABLES Example 3.7.1 Suppose a random variable T has the exponential distribution with parameter λ, and suppose it is observed that T = t, for some fixed value of t. Find the ML estimate, λM L (t), of λ, based on the observation T = t. Solution: The estimate, λM L (t), is the value of λ > 0 that maximizes λe−λt with respect to λ, for t fixed. Since d(λe−λt ) = (1...
View Full Document

This note was uploaded on 02/09/2014 for the course ISYE 2027 taught by Professor Zahrn during the Spring '08 term at Georgia Institute of Technology.

Ask a homework question - tutors are online