Let $m _ { i , j } ( 1 \leqslant i , j \leqslant n )$ be $n ^ { 2 }$ real random variables that are mutually independent, all following the distribution $\mathcal { R }$. The matrix random variable $M _ { n } = \left( m _ { i , j } \right) _ { 1 \leqslant i , j \leqslant n }$ takes values in $\mathcal { V } _ { n , n }$. We set $\tau _ { n } = \operatorname { tr } \left( M _ { n } \right)$.
Calculate the expectation and the variance of the variable $\tau _ { n }$.