grandes-ecoles 2025 Q4

grandes-ecoles · France · mines-ponts-maths1__mp Not Maths
Let $\left( X _ { i } \right) _ { i \in [ 1 , n ] }$ be a sequence of independent random variables all following a Rademacher distribution. Show that $$\forall t \in \mathbf { R } , \quad \operatorname { ch } ( t ) \leq \mathrm { e } ^ { t ^ { 2 } / 2 }$$
Let $\left( X _ { i } \right) _ { i \in [ 1 , n ] }$ be a sequence of independent random variables all following a Rademacher distribution. Show that
$$\forall t \in \mathbf { R } , \quad \operatorname { ch } ( t ) \leq \mathrm { e } ^ { t ^ { 2 } / 2 }$$