Regarding mathematical statistics:

Assume that $($X$1,$ X$2)$ has a bivariate normal distribution where V$($X$1)=$ V$($X$2)=\backslash$sigma $2$ and Cov$($X$1,$ X$2)=0.$ Let

U $=$ X$1+$ X$2$ and V $=$ X$1$ X$2.$ Show that U and V $$ are independent random variables. $($tip: Show that

Cov$($U$,$ V $)=0$ and from this conclude that they are independent.$)$