lec02

lec02.md

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