Consider the following two normal distributions
$f_{1}\left ( x \right )=exp\left ( -\pi x^{2} \right )$
$f_{2}\left ( x \right )=\frac{1}{2 \pi}exp\left \{ -\frac{1}{4\pi }\left ( x^{2}+2x+1 \right ) \right \}$
If $\mu$ and ${\rho}$ denote the mean and standard deviation, respectively, then
- $\mu _{1}<\mu _{2}\:and \:\sigma _{1}^{2}<\sigma _{2}^{2}$
- $\mu _{1}<\mu _{2}\:and \:\sigma _{1}^{2}>\sigma _{2}^{2}$
- $\mu _{1}>\mu _{2}\:and \:\sigma _{1}^{2}<\sigma _{2}^{2}$
- $\mu _{1}>\mu _{2}\:and \:\sigma _{1}^{2}>\sigma _{2}^{2}$