Consider the Gaussian process in Problem $4$ with D $10$ and D $0$:$9.$ Lets conduct the following three experiments pretending that you dont know the true mean $()$ of the process. I strongly recommend using a Python$/$R script or a computer language.$($a$)$ Simulate $400$ independent sample paths, each comprised of n D $104$ observations. For each sample path, compute the $95\%$ CIXntn$1$;$0$:$975$p ; $(1)$ nx Sn$3$ where Xx and S$2$ are the sample mean and sample variance of the respective dataset $($I didnot list the index for the dataset to reduce notation$).$ Report the fraction of the CIs thatcontain $.($b$)$ Repeat the experiment in part $($a$)$ with n D $105$ observations. Does the fraction of the CIs $(1)$that contain increase compared to the outcome of part $($a$)?$ Give a plausible explanation.Hint: use Problem $3.($c$)$ Simulate $400$ independent sample paths, each comprised of n D $104$ observations. For eachsample path, compute the $95\%$ CIXxz p:n $0$:$975$ nReport the fraction of the CIs that contain $.$Explain the outcomes of the experiments in parts $($a$)($c$)$ above$\mathrm{.}6.$ Repeat the experiments in Problem $5($a$)($b$)$ above with D $10$ and D $0$:$9.$ Explain the outcome of these experiments against those in Problem $5($a$)($b$).$