{$$ E = mc^2 $$}
{$$ \mathcal{O}(\log(n)) \equiv \mathbb{E}[1] $$}
{$$ \mathbb{E}[x_{i}]\approx \mu+\sigma\Phi^{-1}\left(\frac{i}{N+1}\right)\left[1+\frac{\left(\frac{i}{N+1}\right)\left(1-\frac{i}{N+1}\right)}{2(N+2)\left[\phi\left[\Phi^{-1}\left(\frac{i}{N+1}\right)\right]\right]^{2}}\right] $$}
{$$ P(a|b) = \frac{P(b|a) \cdot P(a)}(P(b|a) \cdot P(a)) + (P(b|\lnot a) \cdot P(\lnot a)) = \frac{0.05 \cdot 0.9}{((0.05 \cdot 0.9) + (0.95 \cdot 0.1))} = \frac{0.045}{((0.05 \cdot 0.9) + (0.95 \cdot 0.1))} = \frac{0.045}(0.045 + (0.95 \cdot 0.1)) = \frac{0.045}(0.045 + 0.095) = \frac{0.045}{0.14} = 0.32 $$}
{$$ \color{red}{\text{red}}(x) $$}
{$$ \color{blue}{\mathcal{O}(\log(n))} \equiv \color{red}{\mathbb{E}[1]} $$}
