in R code:

$(2$ points$)$ The following gives a vector of $-1\text{'}$s$,0\text{'}$s$,$ and $1\text{'}$s$.$

$>c(0,1,-1,0,1,-1,0,1,-1,0,1)$

$>$rep$(-1$:$1,4)[-1]$

Give two more approaches that return the same vector without using the functions $),$

rep$(),$ and append$().$

$(2$ points$)$ Convert the vector you created in #$1$ into the following character string:

b c a b c a b c a b c

$(2$ points$)$ Convert the vector you created in #$1$ into the following logical vector:

FALSE TRUE TRUE FALSE TRUE TRUE FALSE TRUE TRUE FALSE TRUE TRUE

$(2$ points$)$ Let $\{x_1,$dots,$x_n\}$ be a sample of size $n.$ Type the formula for the sample standard

deviation, and center the equation by writing it within double dollar symbols.

$(2$ points$)$ The $)$ function in R calculates the standard deviation of a sample. Use this

function to compute the standard deviations for the variables "miles per gallon" $($mpg$),$

"number of cylinders" $($cyl$),$ and "displacement" $($disp$)$ within the mtcars dataset.