1. The Exact Measurement company is measuring lengths of objects using laser interference methods. They receive components of lengths 100m, 200m and 300m from a manufacturer. However, the production process is imprecise and the lengths measured do not match exactly the expected component lengths. On BlackBoard, under the section assignments, please find a dataset of 600 length measurements in the file ComponentLengths.xlsx. The resolution of the data is 1m

(a) Plot the raw data and the measurement error data. [6 marks]

(b) Use the data to model the production error, using maximum likelihood and assuming noise is much smaller than the component lengths. Explain your choice of model and parameters. [6 marks]

(c) The manufacturer claims that the production error mean is sampled from a Gaussian of variance 2 = 1(m) 2 and of zero mean. Using this as a prior, calculate the Maximum A Posteriori model of the production noise. [6 marks]

(d) Components that deviate in more than 0.6m from their intended length are classified as faulty. Use the MAP based model to calculate the percentage of faulty components. [7 marks] (25 marks)