P{ z + x*y/(y+a) > x/(x*k+1)}
where x,y,z are exponentially distributed with mean xbar,ybar,zbar.
a,k are constants.
please suggest me how to evaluate this probability.....
for k=0, P lies between 0 and 1 but for any positive value of k, P become higher than one which is unacceptable....
take xbar=1 ybar=3.14 zbar=1
I try to solve this probability but I didn't get its close form so I plot it in matlab for different values of xbar.
But as I take the value of k greater than zero, Probability became larger than one...
Please suggest me something