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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

  1. $\mu _{1}<\mu _{2}\:and \:\sigma _{1}^{2}<\sigma _{2}^{2}$
  2. $\mu _{1}<\mu _{2}\:and \:\sigma _{1}^{2}>\sigma _{2}^{2}$
  3. $\mu _{1}>\mu _{2}\:and \:\sigma _{1}^{2}<\sigma _{2}^{2}$
  4. $\mu _{1}>\mu _{2}\:and \:\sigma _{1}^{2}>\sigma _{2}^{2}$
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