Past exam of the options I course of the University of Oxford / 2010 / O / O2 / b / i / Solution

Put $z_i=e^{-t_i}-c$ and take independent measurement errors ${ϵ}_i\sim N(0,{\sigma }^2)$, independent across the prescribed measurement times. ThenAssume the errors have zero mean so the stated activity curve is the observation mean. Also assume at least two distinct times, making the two design columns linearly independent. The times and the centering constant $c$ are treated as known.