Review of Probability Theory ============================================== Morning session July 16. Afternoon labs are in building 9. Dictionary Cz-En ---------------- - Probability mass function - pravdepodobnostni funkce (for discrete) - Density function - hustota (for continuous) - Cumulative distribution function - distribucni funkce (the same name for continuous and discrete) - False alarms - False positive **TODO understand Poisson distribution** Nice indicator trick: If I want to know probability of $$x \in A$$, I may to introduce indicator function $$1_A(x)$$ where $$1_A(x) = 1 \iff x \in A $$ $$1_A(x) = 0 \iff x \notin A $$ From the equation of Expected value $$ \mathbf{E}(x) = \int_{-\inf}^{\inf} x * f_X(x) d x $$ and $$ \mathbf{E}(g(x)) = \int_{-\inf}^{\inf} g(x) * f_X(x) d x $$ we can simply write $$P(x \in A) = \int_A f_X(x) dx = \int 1_A(x) f_X(x) d x = \mathbf{E}(1_A(x)) $$ TODO go through slides 34 and more Recommended reading ------------------- - K. Murphy "Machine Learning: A probabilistic perspective", MIT - L. Wasserman "All of statistics: Concise Course