TP#18_f08 - CE 3102 Fall 2008 Thought Problem 18 Left Turns...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
CE 3102 Fall 2008 Thought Problem 18 Left Turns (Again) A traffic engineer wants to know the fraction of vehicles making a left turn from an intersection’s westbound approach. During an afternoon peak hour the engineer counts a total of 215 vehicle’s arriving at this approach, and of these 55 turned left. (a) Compute the method of moments (MOM) estimate of p? (b) Is this a good estimate? (c) How accurate is this estimate? (d) Compute the maximum likelihood estimate of p.
Background image of page 1

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

View Full DocumentRight Arrow Icon
CE 3102 Fall 2008 Thought Problem 18 Instructor’s Partial Solution (a) Let X denote the number of left-turns made during the PM peak hour. If we assume that each driver makes his/her left turn decision independently of the other drivers, and that each has an (unknown) probability p of making a left turn, then X can be modeled as a binomial random variable with n=total arrivals, and p=left-turn probability. We’ve observed n=215 and X=55, and want to estimate p. In this case, we know the expressions for the mean and variance of X E[X]=np Var[X]=np(1-p). Method of moments estimation would then equate the observed value for X to its
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This document was uploaded on 02/05/2011.

Page1 / 4

TP#18_f08 - CE 3102 Fall 2008 Thought Problem 18 Left Turns...

This preview shows document pages 1 - 3. Sign up to view the full document.

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