$1.$ The random variable X has density function

f $.$x$/$ D

$(1$

$4$ ex ; x $<0$

$3$

$4$ ex ; x $0$:

$($a$)$ Find the c$.$d$.$f$.$ of X $.$

$($b$)$ Use the inverse$-$transform method to derive a formula for generating realizations of X $.$

$($c$)$ Create a script to generate $1000$ realizations of X from part $($a$).$ Then use the latter real$-$

izations to generate a histogram; this histogram should resemble the density function f $./.$

Feel free to use any package $($e$.$g$.,$ Python or R$)$ and the default random number generator.

You can also use an Excel spreadsheet