grandes-ecoles 2023 Q12

grandes-ecoles · France · centrale-maths2__official Normal Distribution Tail Bound or Concentration Inequality Proof
Deduce a simple equivalent of $1 - \Phi ( x )$ as $x$ tends to $+ \infty$, where $\Phi ( x ) = \int _ { - \infty } ^ { x } \varphi ( t ) \mathrm { d } t$ and $\varphi ( x ) = \frac { 1 } { \sqrt { 2 \pi } } \mathrm { e } ^ { - x ^ { 2 } / 2 }$.
Deduce a simple equivalent of $1 - \Phi ( x )$ as $x$ tends to $+ \infty$, where $\Phi ( x ) = \int _ { - \infty } ^ { x } \varphi ( t ) \mathrm { d } t$ and $\varphi ( x ) = \frac { 1 } { \sqrt { 2 \pi } } \mathrm { e } ^ { - x ^ { 2 } / 2 }$.