$($b$)$ One thousand observations were simulated from a complicated but known

continuous distribution. The data are shown in the histograms below, with

various superimposed curves. The true PDF is shown in panel $($a$).$ The

urve in panel $($b$)$ corresponds to a parametric density estimate using the

Gaussian distribution. Finally, the result of KDE using R$$s density$()$

function with different choices of kernel and bandwidth $($bw$)$ are shown

in the four remaining panels.

i$.$ Briefly discuss whether the parametric density estimate in panel $($b$)$

is a good fit for the true PDF in panel $($a$).[3$ marks$]$

ii$.$ Discuss the influence that the choices of bandwidth and kernel can

have on KDE in the context of this simulation study. Refer to panels

$($c$),($d$),($e$),$ and $($f$)$ of the plots above in your answer. $[9$ marks$]$