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Homework Help: Probability- Transformation of variable

  1. Oct 23, 2008 #1
    Following is the
    question
    http://tinyurl.com/62uxof
    solution
    http://tinyurl.com/6m4lcc

    The distribution in question means cumulative distribution.

    What I do not understand in the solution is the step from P{X_1<=wX_2} to the integration formula that followed immediately. May I know the reasoning for it?
     
    Last edited: Oct 23, 2008
  2. jcsd
  3. Oct 23, 2008 #2

    tiny-tim

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    Science Advisor
    Homework Helper

    Hi jack1234! :smile:

    P(X ≤ wY) = lim ∑P(X ≤ wY | v ≤ Y ≤ v + dv)P(v ≤ Y ≤ v + dv)

    = ∫P(X ≤ wv)dP(Y ≤ v) :wink:
     
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