(a) A nonlinear model has often to be fitted to the input and output data from a measuring system. Describe briefly what is meant by a nonlinear model and give an example. [20%]

(b) If = (), where = (1,2, ... , )T is estimated by with covariance matrix , what is the estimate of = (1, 2, ... , )T and its covariance matrix as given by the law of propagation of uncertainty (multivariate LPU)? [30%]

(c) Given two masses M1 and M2 measured with the estimates m1 and m2, and the standard uncertainties of 1 and 2, respectively. Assume M1 and M2 are independent, what is the estimate of M1+M2 and its standard uncertainty? [30%]

(d) What will be the estimate and the associated standard uncertainty of the difference M1-M2 of the two gauge block lengths in c)? [20%]