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