Directions
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
1 Pni=1(xi − x¯)4
g2 = 1nPn (xi − x¯)22 − 3
i=1 n
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
Pr
R =
1 − (1 + r)−n
(a) Construct a function which employs this formular
(b) Calculate Jane’s monthly payments, if the initial amount is $100,000, the interest rate is 1% and the number of interest conversions periods is 300.
4. Suppose payments of P dollars are deposited annually into a bank account which earns constant interest r per year. What is the accumulated value of the account at the end
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Lesson 13: Homework STAT/BIOS 823: Writing R functions
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 (1 + r)n − 1
n−1
Amount = P(1 + r) + ··· + P(1 + r) + P = P
r
(a) Write an R function to compute the accumulated amounts after n = 10 years, with periodic payments P = $400 with a vector of interest rates r ranging from
0.01 to 0.2 by increments of 0.01.
(b) Produce a line plot of the amounts (y-axis) against the interest rates (x-axis)
(c) Optional question: Write a single function to perfom both parts (a) and (b) above.
