Inverse Transform Method

Discussion in 'CS1' started by Sunil Chaudhary, Feb 23, 2022.

  1. Sunil Chaudhary

    Sunil Chaudhary Active Member

    Hi,
    Under Inverse Transform Method For Continuous Distributions, the study material mentions sort of proof concluding as:
    P[U<=F(x)] = F(x)

    Could someone please elaborate on above final conclusion as I am unable to understand the same.

    Thanks.
    Sunil
     
  2. Julie Lewis

    Julie Lewis ActEd Tutor Staff Member

    The distribution of U is U(0,1). So the CDF of U is F(u) = P(U <= u) = u. Hence P(U <= F(x)) = F(x).

    You might find it helpful to consider a numerical example. If U is uniformly distributed over the interval (0,1), then U can take any value between 0 and 1, and each value is equally likely. So, P(U < 0.5) = 0.5, P(U <0.8) = 0.8, etc.
     
  3. Sunil Chaudhary

    Sunil Chaudhary Active Member

    Thanks Julie.

    Sunil.
     

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