Question

If X has distribution function F, what is the distribution function of $e^X$?

Short answer

In the given information The distribution of $e^X$can be written as composition of logarithm function and distribution function of X

Step-by-step solution

Step 1:Given Information

Take any $a\in supp{e}^X$(the support of $e^X$is not specified since we are not given the support of X ).We have that

$F_{e^X}\left(a\right)=P\left(e^X\le a\right)=P(X\le \log (a\left)\right)=F_X\left(\log a\right)$

Explanation

$e^X$can be written as composition of logarithm function and distribution function of X

Final Answer

The distribution of $e^X$can be written as composition of logarithm function and distribution function of X