In order for the estimator to be unbiased, the expected value must be equal to the true value, which gives
(4.6)The expected value of the estimator ̂μ is
It is unbiased if
(5.1)The inverse mapping is not unique, therefore the inference from y to x is ill-posed.
(5.2)The system of equations to solve this problem is over-determined, since there are more data points (N < 2) than degrees of freedom (a,b). This means that in general there is no solution that interpolates all data points. Therefore, the problem is ill-posed.
The following variation is well-posed.
Find the parameters ...