I've never come across one quite this complicated.
Am I right in saying you would first need to integrate to get FX(x)
Nevermind solved the question. However how do we know about the 1 in 1-e^-x. I understand that you lose it when you differentiate to find fX(x) but how can we explain the existence of it?
Function of a random raviable - density function Watch
- Thread Starter
Last edited by TomLeigh; 09-12-2010 at 21:38.
- 09-12-2010 21:25
- 09-12-2010 22:36
The way to think about it is this.
We know the density function of Y is the derivative of the distribution function of Y, so it suffices to find the distribution function.
This is F_Y(y) = P(Y < y) = (using what we are given) P(X^b < y) = P(X < y^(1/b)) [note we aren't doing anything "wrong" here because b is positive].
Hang on, we can find P(X < y^(1/b)), this is merely . Can you finish him?