$($b$)$ Three thousand observations were simulated from a complicated generalised inverse Gaussian distribution. The data are shown in the histograms on the next page, with various superimposed curves. The true PDF is shown in panel $($a$).$ The curve in panel $($f$)$ corresponds to a parametric density estimate using the Gaussian distribution. Finally, the result of KDE using R$\text{'}$s density function with different choices of kernel and bandwidth $($bw$)$ are shown in the four middle panels.

i$.$ Briefly describe the steps you would take in R to create a parametric Gaussian density estimate plot like the one from panel $($f$).$

$[4$ marks$]$

ii$.$ Discuss the influence that the choices of bandwidth and kernel can have on KDE in the context of this simulation study. Solve by hand Refer to all six plots throughout your answer.

$[10$ marks$]$