Well you could use the but I guess that is defined by integration...
Oh wait! I remember how to do this:
Here is an example:
Differentiating the density identity (ofcourse I'm assuming we can swap the order of differentiation and integration).
Which simplifies to
Where the last equality holds by an identity
Thank you for the response, but I'm not quite following. Can you use the following as an example and find the mean using the method you described using no integration:
pdf: fx(X) = ((x-5)^3)/4 for 5 <= x <= 7 and 0 elsewhere
cdf: Fx(X) = ((x-5)^4)/16 FOR 5 <= x <= 7