Bayes' Rule

 

Normal Distribution - Probability Distribution Function

 Probability Distribution Function, Normal: $X\sim <!--\; \sim \; -->\mathcal{N}(\mathrm{\mu <!--\; \mu \; -->},{\mathrm{\sigma <!--\; \sigma \; -->}}^2)$

,  -∞ < x < ∞ ,   -∞ < μ <  ∞ , σ > 0

$\mathrm{\mu <!--\; \mu \; -->}=E[X]\; ,{\mathrm{\sigma <!--\; \sigma \; -->}}^2=Var(X)$

 

 

The function is called standard normal when $\mathrm{\mu <!--\; \mu \; -->}=0$  and  $\mathrm{\sigma <!--\; \sigma \; -->}=1$ then $Z\; =\frac{X-\mathrm{\mu <!--\; \mu \; -->}}{\mathrm{\sigma <!--\; \sigma \; -->}}$