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Homework Help: Cumulative distribution transformation

  1. Sep 28, 2012 #1
    1. The problem statement, all variables and given/known data

    Let [itex]F[/itex] be the cumulative distribution function of a random variable [itex]X[/itex]. Find the cumulative distribution function of [itex]Y= {\alpha}X+\beta, where \, \alpha \gt 0[/itex]

    2. Relevant equations

    3. The attempt at a solution
    I think this a fairly easy question, I just want to make sure I understand:
    [itex]F(x)=P(X \leq x)=P(\dfrac{Y-\beta}\alpha \leq x)=P(\dfrac{Y-\beta}\alpha \leq y)=F(y)[/itex]
  2. jcsd
  3. Sep 29, 2012 #2
    I'm thinking I made one small mistake:
    [itex]F(x)=P(X \leq x)=P(\dfrac{Y-\beta}\alpha \leq x)=P(Y\leq y)=F(y)[/itex]
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