A colleague defines a random variable $X = \frac{Z}{Y^2}$, where $Z$ is a known normal random variable, $Y$ is a known gamma random variable, and $Z$ and $Y$ are independent of each other. You are not able to get an analytical form for the cumulative distribution function for $X$, but you need to find the approximate 90th percentile of $X$. How do you go about doing this?
Gamma random variable , need to find the approximate 90th percentile of X?
distribution
In  R:> Z = function(n){rnorm(n)} # normal(0,1) here> Y = function(n){rgamma(n,10,10)} # some gamma variable> quantile(Z(100000)/Y(100000)^2,.9) # 100000 from your target dist     90% 1.635033 So 90% of the values are less than 1.635