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# Function of a random raviable - density function Watch

1. 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?
2. 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?

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