IEOR 165 Lecture 6 June 4 2009

IEOR 165 Lecture 6 June 4 2009 - Lecture Notes IEOR 165 |...

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

View Full Document Right Arrow Icon
Lecture Notes IEOR 165 | George Shanthikumar Tu W Th 2-4:30 pm | 3113 Etcheverry Based on graphical interpretation, we can decide that = . AMLE a certain xminor xmax And then we solve for = [ ] EAMLE E Xminor max = + If EAMLE nn 1a then this is a biased estimator : So we multiply : = + = + . AMLE c n 1nAMLE n 1nxmin is an unbiased estimator of a To decide which is better estimator, we see which variance is smaller. Estimation & Hypothesis Testing of Bernoulli Population Effectiveness of an ad campaign. (find statistically significant improvement) Let x be a {0,1} r.v. (Bernoulli r.v.) with probability of success P (=P{x=1}) Suppose we have a sample ,…, . x1 xnand we want to estimate P Estimate P: (use average) = = = = Ex ppMOM xbar 1nk 1nxk : = = - - = Lx p pk 1nxk1 pn k 1nxk Understanding that = - , = fxx 1 p x 0 = , = = * + = * - = + ( - )( - ) fxx p x 1Ix 1 p Ix 1 1 p xp 1 x 1 p So if we have a vector (1 0 0 1 1 0 0 0 1), then we multiply by P*(1-p)(1-p)p*p*(1-p)(1-p)(1-p)*p So if we take the log of likelihood function:
Background image of page 1

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

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 07/22/2009 for the course IEOR 165 taught by Professor Shanthikumar during the Summer '08 term at University of California, Berkeley.

Page1 / 3

IEOR 165 Lecture 6 June 4 2009 - Lecture Notes IEOR 165 |...

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