Using R Provide the code that parallelizes the following:

library$($MKinfer$)$ # Load package used for permutation t$-$test

# Create a function for running the simulation:

simulate$\_$type$\_$I $<-$ function$($n$1,$ n$2,$ distr, level $=0\mathrm{.}05,$ B $=999,$alternative $=$ "two.sided", $...)$

$\{$

# Create a data frame to store the results in:

p$\_$values $<-$ data.frame$($p$\_$t$\_$test $=$ rep$($NA$,$ B$),$p$\_$perm$\_$t$\_$test $=$ rep$($NA$,$ B$),$p$\_$wilcoxon $=$ rep$($NA$,$ B$))$

for$($i in $1$:B$)$

$\{$

# Generate data:

x $<-$ distr$($n$1,...)$

y $<-$ distr$($n$2,...)$

# Compute p$-$values:

p$\_$values$[$i$,1]<-$ t$.$test$($x$,$ y$,$

alternative $=$ alternative$)$$p$.$value

p$\_$values$[$i$,2]<-$ perm.t$.$test$($x$,$ y$,$alternative $=$ alternative,R $=999)$$perm.p$.$value

p$\_$values$[$i$,3]<-$ wilcox.test$($x$,$ y$,$alternative $=$ alternative$)$$p$.$value

$\}$

# Return the type I error rates:

return$($colMeans$($p$\_$values $<$ level$))$

$\}$

Provide the code that runs the following code in parallel with $4$ workers $($with mclapply$)$:

lapply$($airquality$,$ function$($x$)\{($x$-$mean$($x$))/$sd$($x$)\})$