Problem $5.$ Verify the following facts:

$($i$)$ If a r$.$v$.NB(n,p),$ then,

$E[N]=np,$Var$[N]=np(1-p)$

$($ii$)$ If a r$.$v$.T{T}_n,$ then,

$E[T]=0,$ and $,-F^{-1}()=F^{-1}(1-),$ for any $in(0,1).$