I am trying to obtain outage probability for the given expression but not getting it clearly.
$P_o = \text{Pr}\biggl(XY \leq \frac{\gamma_t(\mu_3Z+\mu_4)}{\zeta-\frac{\gamma_t \mu_1}{Y}-\frac{\gamma_t \mu_2}{X}}\biggr)$, where $X,Y,Z$ are independent exponential random variables having CDF $F_X(x), F_Y(y), F_Z(z)$ and PDF $f_X(x), f_Y(y), f_Z(z)$ and all other things are constant.
I further wrote it as
$P_o = \int_0^{\infty} \int_0^{\infty} \int_0^{\infty} \text{Pr}\biggl(XY \leq \frac{\gamma_t(\mu_3Z+\mu_4)}{\zeta-\frac{\gamma_t \mu_1}{Y}-\frac{\gamma_t \mu_2}{X}}\biggr)f_X(x) f_Y(y) f_Z(z)\text{d}x \text{d}y \text{d}z ?$
Any help in this regard would be highly appreciated.