When the lifetimes X$1,$ X$2,...$ have the gamma density function

f $($x$)=$ xe$$x

for x $>0,(4)$

then the waiting times Wn $=$ X$1++$ Xn have the gamma density

fn$($x$)=$ x

$2$n$1$

$(2$n $1)!$e

$$x

for x $>0$prove provproopppp$[$p