# Homework Help: Cumulative distribution transformation

1. Sep 28, 2012

### mrkb80

1. The problem statement, all variables and given/known data

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

2. Relevant equations

3. The attempt at a solution
I think this a fairly easy question, I just want to make sure I understand:
$F(x)=P(X \leq x)=P(\dfrac{Y-\beta}\alpha \leq x)=P(\dfrac{Y-\beta}\alpha \leq y)=F(y)$

2. Sep 29, 2012

### mrkb80

I'm thinking I made one small mistake:
$F(x)=P(X \leq x)=P(\dfrac{Y-\beta}\alpha \leq x)=P(Y\leq y)=F(y)$