$(1)$ Consider the following distribution function, F$($x$)=$ x $$ x$,0$ x $1.($i$)$ Find the inverse function of F$($x$)$ using r code $[2].($ii$)$ Generate $1000$ random numbers using the inverse function from $($i$)$ and display the distribution in a histogram $($you may adapt code from the lecture note or you can create your own$)[3].(2)$ Manitoba$$s vehicle registration plate number consists six charecters $($three letters followed by three numbers$)($i$)$ Create an R function reg.vehicle$()$ to generate n vehicle registration plate numbers $($Hint: you may adapt the code to generate the postal code from the lab material and change as necessary$)[2].($ii$)$ Generate $10000$ vehicle registration plate numbers using function reg.vehicle$()$ and print the head of the dataframe. Pease set.seed$(1234)$ to generate same samples $[2].($iii$)$ Since Manitoba has multicultural society, and therefore, people in some religions do not want the vehicle registration plate number which has the first number zero. Your manager at Manitoba$$s transportation office asked you to separate the registration plate that contain the first number zero. Write an R code to separate the data frame generated in $($ii$)$ containing the first number zero and print the head of the dataset $[3].($iv$)$ One of your friend$$s family wants an easy number to start with $1$ and end with $0.$ How many possible numbers do you have to offer your friend? $[3]$