Consider the dataset HW$2$ which has many columns including two that are named

$\text{'}A\text{'}$ and $\text{'}B\text{'}$ consisting of numeric values that has been loaded into Rstudio.

Specify Rstudio code $($one line$)$ which could be used to accomplish the following:

a$.$ Multiply every entry of $B$ by the corresponding row entry in $A.$

b$.$ Print the relative standing $($see earlier lecture for formula$)$ of each

observation in B $($treating it as a population$).$

c$.$ Create an new object$/$vector $($call it whatever you want$)$ that contains the

last $5$ values in B$.$

d$.$ Create a new object called "ColVariances" which is a vector which contains

the $($sample$)$ variances of each column A and B$.$

Hint: You know how to create objects. You know how to compute the

variances of each column. You know how to merge two numbers $($in this

case the columns means$).$

e$.$ Create a for$()$ loop that outputs a vector containing the products of every

entry in column A with the preceding entry in column A $($starting from the

$2^{nd}$ row$).$

Hint: We did something similar when creating returns.

Hint: You can create a dataset using the following code to test out your answers:

MYDATA$=$data. frame $(A=c(1,3,2,4,5),B=c(5,10,20,15,25))$

Note: You are being asked for the code in this problem, not the output.