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Unformatted text preview: CE 3102 Fall 2008 Thought Problem 19 Maximum Likelihood and Confidence Intervals Let’s return to the situation in Thought Problem 17, where a traffic engineer has obtained a sample of speeds of vehicles approaching an intersection: 33, 32, 33, 30, 27, 35, 34, 38, 46, 39 What we want to do now is: (a) Compute the maximum likelihood estimate of the mean speed, (b) Admitting that its unlikely that the estimated mean exactly equals the (unknown) population mean, determine a range of values that is likely to contain the population mean. By “likely to contain” we mean that the probability this range contains the mean is equal to 0.90.Assume that the speed variance is known, and equal to 25 (mph) 2 . (c) What sample size is needed to guarantee, with 90% confidence, that our interval contains the mean? CE 3102 Fall 2008 Thought Problem 19 Instructor’s Partial Solution (a) Let X i denote the random variable we believe generated speed observation i . That is Observations: x 1 x 2 … x n...
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This document was uploaded on 02/05/2011.
- Spring '11