Using R Markdown in R Studio, complete the following questions Write an R function for computing the value of f (x) = e−x2

Using R Markdown in R Studio, complete the following questions. Launch RStudio and open a new RMarkdown file or use the class RMarkdown template provided and save it on your working directory as a.Rmd file. At the end of the activity, save your pdf generated from RMarkdown+Knitr and submit your homework on the Blackboard.

If you have questions, please post them on the lesson’s Discussion Board.

All questions are mandatory. R code and output must be clearly shown.

Homework submitted after the due date will attract a penalty of 10 points per day after the due date.

1.    Write an R function for computing the value of f (x) = e−x2 and test it for a vector x = c(0, 1, 100).

2.    Write an R function to compute the sample excess kurtosis given by for a given vector x = (x1, xn), where x¯ is the average of the elements of x.  Test the function for a vector x = 1:10.

3.    Suppose Jane wishes to take out a mortgage on a house. She wants to know what her periodic payments will be. If P is the initial amount mortgaged, r is the effective interest rate, and n is the length of the mortgage, then the periodic payment R is given by R=Pr1 − (1 + r)−n

(a)      Construct a function which employs this formula

(b)      Calculate Jane’s monthly payments, if the initial amount is $100, 000, the interest rate is 1% and the number of interest conversion periods is 300.

4.    Suppose payments of P dollars are deposited annually into a bank account that earns constant interest r per year. What is the accumulated value of the account at the end of n years, supposing deposits are made at the end of each year? The total amount at the end of n years is given by the expression Amount = P (1 + r)n−1 + · · · + P (1 + r) + P = P  (1 + r)n − 1r