Lab Goal: The simple goal of this lab is to get you thinking about R and RStudio again. It is not meant to be an introduction to R.

This lab can be completed using only R and without RStudio, but you should really use RStudio. For reference material, see Applied Statistics with R chapter two through six.

Basic Calculations

[Exercise] Calculate \(e^2\).

[Exercise] Calculate the natural log of 3.

Getting Help

y = c(0, 2, NA, 3, 4, 1, 9, 0)

[Exercise] Calculate the mean of y with the missing values removed. Use only the mean() function.

Packages

[Exercise] Run the following code:

ggplot(mpg, aes(x = reorder(class, hwy), y = hwy, fill = class)) + 
  geom_boxplot() +
  xlab("class") +
  theme(legend.position = "none")

To do so, you will need to make sure the ggplot2 package is installed, and loaded.

[Exercise] Modify the following code to run, but without loading the entire MASS library. The lda() function is from the MASS package.

lda(Species ~ ., data = iris)$means

Vectors and Lists

x = 1:100

[Exercise] Calculate

\[ \sum_{i = 1}^{n} \ln(x_i). \]

That is, sum the natural log of each element of x.

[Exercise] After running the following code, how many of the elements of some_vector are larger than 1? A good solution will use only one line of code.

set.seed(42)
some_vector = rnorm(100)

Probability

[Exercise] Consider a random variable \(X\) that has a normal distribution with a mean of 5 and a variance of 9. Calculate

\[ P[X > c], \]

for \(c = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.\)

Style

The following code is “correct” but terrible. Don’t write code like this!

set.seed(1337);mu=10;sample_size=50;samples=100000;
x_bars=rep(0, samples)
for(i in 1:samples)
{
x_bars[i]=mean(rpois(sample_size,lambda = mu))}
x_bar_hist=hist(x_bars,breaks=50,main="Histogram of Sample Means",xlab="Sample Means",col="darkorange",border = "dodgerblue")
mean(x_bars>mu-2*sqrt(mu)/sqrt(sample_size)&x_bars<mu+2*sqrt(mu)/sqrt(sample_size))

[Exercise] Fix this code! You don’t need to change how the code accomplishes the task, but you should update the style.