$1.$ From ISLR obtain the Caravan data. Please answer the following questions based on this dataset. Here is what the dataset is:

$\backslash$table$[[4,$A$,$B$,$C$,$D$],[1,$Name,Age,Weight,Height$],[2,$A$,1,2,4],[3,$B$,2,2,2],[4,$C$,2,4,6\mathrm{.}2],[5,$D$,22,4,6],[6,$E$,19,185,5\mathrm{.}9],[7,$T$,5,6,7],[8,$K$,56,76,78],[9,$U$,7666,8,7]]$

a$)$ Name Caravan data as temp$1.$

b$)$ Find the dimension of Caravan data.

c$)$ Find column names of Caravan data.

d$)$ Find the rows of the Caravan where the Purchase column shows Yes.

e$)$ Find the rows of the Caravan where the Purchase column shows No and the MOSTYPE value isless than $25.$

f$)$ Obtain the subset of the Caravan data where the column names include $$M$.$

g$)$ Obtain the subset of the Caravan data where the column names start with $$M$.$Hint: For this problem, you can use, dplyr library and the following code below.select$($temp$1,$starts$\_$with$("$M$"))$

$2.$ For this question, you need to use airquality data. You can access this data from R without anylibrary. This data includes some missing values which are shown as NA in the data set.

a$)$ Find total number of missing values.

b$)$ Find how many missing values are in each column.

c$)$ Delete the rows which contains missing data.

d$)$ Find the rows where Solar.R column includes missing values and remove these rows.

e$)$ Find the rows where Ozone column includes missing values and remove these rows.

f$)$ Find the rows where Solar.R and Ozone columns include missing values and remove these rows.

g$)$ Find the rows where Solar.R or Ozone columns include missing values and remove these rows.

$3.$Gaussian random numbers. One way to generate a random number taken from the Gaussian distribution is to use the Box$-$Muller formula:

$Z=sin(2v)(-2lnu{)}^{\frac{1}{2}}$

where u and v are real numbers between $0$ and $1$ generated by runif$(1,0,1)$function$.$ Compose a program that writes a standard Gaussian random variable. And calculate Z value.