Let $\left( X _ { i } \right) _ { i \in [ 1 , n ] }$ be a sequence of independent random variables all following a Rademacher distribution. Show that: for all $t \geq 0$, for all $\left( c _ { 1 } , \ldots , c _ { n } \right) \in \mathbf { R } ^ { n }$,
$$\mathbf { E } \left( \exp \left( t \sum _ { i = 1 } ^ { n } c _ { i } X _ { i } \right) \right) \leq \exp \left( \frac { t ^ { 2 } } { 2 } \sum _ { i = 1 } ^ { n } c _ { i } ^ { 2 } \right)$$