Let $U_i,1i3,$ be i$.$i$.$d$.$ Uniform$(0,1$Let Ui

i be i$.$i$.$d$.$ Uniform$(0,1)$ random variables. Let X :$=$ min i Ui i$/3\},$

and, given X $=$ x$,$ Y has Binomial$($x$,1/3)$ distribution. Write down the marginal pmf P$[$Y $=$ y$]$

of Y$,$ and estimate E$($Y

$2$

$)$ based on $100$ iid copies of Y$,$ to be generated by

$($a$)$ inverse$-$transform method $($Binomial $($n$,$ p$)$ pmf at x in $\{0,1,...,$ n$\}$ may be computed as

dbinom $($x$,$n$,$p$)).$

$($b$)$ composition method Please use R programming language for both and write detailed explanation on the pmf part