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**I-Think** Not sure of my understanding, so asking for help

2 part question

If $\displaystyle X$ has a distribution function $\displaystyle F$

a) What is the distribution function of $\displaystyle e^X$

b) What is the distribution function of $\displaystyle \alpha{X}+\beta$, where $\displaystyle \alpha$ and $\displaystyle \beta$ are constants, $\displaystyle \alpha \neq{0}$

Solution attempts

I know that

$\displaystyle F(x)=P[X\leq{x}]$

and $\displaystyle F(a)=\sum_{all x\leq{a}} p(x)$

Therefore, should I say that $\displaystyle F(x)=P[X\leq{e^x}]$ (ditto for part b) and continue from there? But I'm not sure how to continue, so help please