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Function of a random raviable - density function Watch

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    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?
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      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 \displaystyle \int_0^{y^{1/b}} \text{f}_X(x) \text{d}x. Can you finish him?
     
     
     
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