[Solved] STAT823 Homework 13-Writing R Functions

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.

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, ,x_n), 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

• Construct a function which employs this formular
• Calculate Janes 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

n1

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.

• Produce a line plot of the amounts (y-axis) against the interest rates (x-axis)
• Optional question: Write a single function to perfom both parts (a) and (b) above.