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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]