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Thread: transformation problem

  1. #16
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    Re: transformation problem




    To sum up, if Y = F_X(X), X is a continuous random variable,

    then F_Y(y) = \Pr\{Y \leq y\} = \Pr\{F_X(X) \leq y\}
= \Pr\{X \leq F^{-1}_X(y)\} = y, y \in [0, 1]

    \Rightarrow Y \sim \mathrm{Uniform}(0, 1)

    This is just the key result in inverse transform sampling for simulation.

  2. #17
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    Re: transformation problem


    So the variable Y follows an Uniform(0,1) distribution?

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