diff --git a/ex-5/casino b/ex-5/casino new file mode 100755 index 0000000..6da0aae Binary files /dev/null and b/ex-5/casino differ diff --git a/ex-5/manual b/ex-5/manual new file mode 100755 index 0000000..fea418c Binary files /dev/null and b/ex-5/manual differ diff --git a/ex-5/trifecta b/ex-5/trifecta new file mode 100755 index 0000000..9addaef Binary files /dev/null and b/ex-5/trifecta differ diff --git a/notes/sections/4.md b/notes/sections/4.md index 55a07db..c0ae280 100644 --- a/notes/sections/4.md +++ b/notes/sections/4.md @@ -231,8 +231,24 @@ Cramér-Rao bound. The following results were obtained: $$ - p_{\text{max}} = 10 \pm 0.016 \with \chi^2 = 0.072 + p^{\text{oss}}_{\text{max}} = 10.005 \pm 0.018 \with \chi^2 = 0.071 $$ +In order to compare $p^{\text{oss}}_{\text{max}}$ with the expected value +$p_{\text{max}} = 10$, the following compatibility t-test was applied: + +$$ + p = 1 - \text{erf}\left(\frac{t}{\sqrt{2}}\right)\ \with + t = \frac{|p^{\text{oss}}_{\text{max}} - p_{\text{max}}|} + {\Delta p_{\text{max}}} +$$ + +where $\Delta p_{\text{max}}$ is the absolute error of $p_{\text{max}}$. At 95% +confidence level, the values are compatible if $p > 0.05$. +In this case: + + - t = 0.278 + - p = 0.781 + which allows to assert that the sampled points actually follow the predicted distribution.