Activity 2

Define mathematically the mean square error of a position estimate. Explain and justify your answer.

The MSE is defined almost the same as variance, given by


\frac{\sum{(x-\overline{x})^2}}{n}

Activity 3

Prove that the following holds for Gamma distribution:


\alpha = \frac{\overline{x}^2}{s^2}


\beta = \frac{s^2}{\overline{x}}

Which results by substition from the following:

\overline{x} = \alpha \beta, \quad s^2 = \alpha \beta^2


\alpha \left(\frac{\overline{x}}{\alpha}\right)^2 = s ^2

yielding the first definition for \alpha. Substituting into the expression for \beta results in


\beta = \frac{\overline{x}}{\alpha} = \frac{\overline{x}}{\frac{\overline{x}^2}{s^2}} = \frac{s^2}{\overline{x}}