Cumulative distribution transformation

  • Thread starter mrkb80
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  • #1
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Homework Statement



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]

Homework Equations





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]
 

Answers and Replies

  • #2
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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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