Even Function

$$\mathbb{E}(x)=\frac{f(x)+f(-x)}{2}$$ $$\mathbb{E}(-x)=\mathbb{E}(x)$$ $$\int f(t)\mathbb{E}(t)dt=\int f_{\mathbb{E}}(t)\mathbb{E}(t)dt$$

• Sum of even functions is even
• Product of even functions is even
• Product of an even and odd is an Odd Function