Let $p \in \left[ 1 , + \infty \right[$. Let $\left( X _ { i } \right) _ { i \in \llbracket 1 , n \rrbracket}$ be a sequence of independent random variables all following a Rademacher distribution. Let $\left( c _ { 1 } , \ldots , c _ { n } \right) \in \mathbf { R } ^ { n }$. Assume $1 \leq p < 2$. Justify that there exists $\theta \in ] 0,1 [$ such that $\frac { 1 } { 2 } = \frac { \theta } { p } + \frac { 1 - \theta } { 4 }$.