Originally Posted by

**joop** Would you please explain to me how you got

$\displaystyle \int_{0}^{\infty} (1- \int_{0}^{x} f_T(t)\, dt )\, dx $

$\displaystyle = \int_{0}^{\infty} \int_{x}^{\infty} f_T(t)\, dt \, dx$

To the best of my understanding,

$\displaystyle \int_{0}^{\infty} (1- \int_{0}^{x} f_T(t)\, dt )\, dx $

$\displaystyle = \int_{0}^{\infty} \, dx - \int_{0}^{\infty} \int_{0}^{x} f_T(t)\,dt \,dx$

and reversing the order,

$\displaystyle = \int_{0}^{\infty} \, dx - \int_{0}^{\infty} \int_{t}^{\infty} f_T(t)\,dx \,dt$ Mr F says: I'd be interested to see how you do the first integral ......

Thanks in advance.