That's a standard property, if Fy has an inverse (it's the case in particular if the rv has a continuous density).
Indeed : , for since is a probability and is hence taking values between 0 and 1.
I am going through an example where one needs to find score and information for a random sample of size n from the logistic distribution with a density function
and the score is
then the explanation goes, 'by recognising that we can calculate information... and they use the formula for Var of a Uniform distribution.
Can someone help me to see that ?