What is the CDF of the following:
P$($$a_m$ $Z_m$ - $K$ $\sum^{M}_{i=m+1}$ $a_i$ $X_i$$ $<$ C$$)$
where $Z_m$ and $X_i$ are independent and identically distributed random variables, continuous positive random variables that take value ranging from $0$ to infinity (decimals included). having the following CDF:
$F_{Z_m}(z){=}\frac{\gamma\left(B,\frac{\sqrt{z}} {u}\right)}{\Gamma(B)}$
$F_{X_i}(x){=}\frac{\gamma\left(B,\frac{\sqrt{x}} {u}\right)}{\Gamma(B)}$
$a_m$, $a_i$, $K$, $u$ and $C$ are constants. where $M=6$.