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# Lab 11 - CE 93 Spring 2011 Prof Joan Walker CE 93 Lab 11...

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CE 93 Spring 2011 Prof. Joan Walker 1 CE 93 Lab 11 (Apr 13, 2011) Part I) Illustration of maximum likelihood estimation The number of accidents occurring weekly on a particular stretch of a highway has a Poisson distribution. From historical data we randomly picked ten weeks records, as follows: 4 3 5 0 2 4 6 1 3 4 1. What are the likelihood function and log-likelihood function? 2. Determine the maximum likelihood estimator of the parameter λ . 3. Plot L( λ ) and LL( λ ) respectively against λ , for values of λ ranging from 1 to 10. You will observe the log transformation does not change the point where the maximum value in the respective functions is achieved. Part II) Confidence interval of unknown parameters of Normal distribution Suppose that we know that the concrete cube compressive strength (in N/mm^2) at 28 days is normally distributed, and you measured ten such cubes whose compressive strengths are 64.9, 48.6, 69.1, 78.2, 55.1, 70.6, 74.5, 46.1, 47.6, 67.7.

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