Lab 3: Programming Fundamentals

Total Points: 35

Part 1. Loops and Iterations (5+5 pts)

1. Generate a vector norm_vec with length \(n=1000\) from the normal distribution with mean 1 and variance 5.

• Write a for() loop with if() statement to count the number of entries in norm_vec that are strictly larger than 0.

• Re-do the above task without using any for() loop (i.e., apply the build-in function in R with logical vector operation).

• Is the execution time of using for() loop longer than the vectorization? (Return a logical TRUE/FALSE).

set.seed(123)  ## Don't change this line. It makes the result reproducible.
# Your code here

2. Keep generating a pair of integers from the binomial distribution \(\mathrm{Bin}(30, 0.3)\). How many times did you generate the pair of integers until both integers are equal? (Implement it in two methods: while and repeat.)

set.seed(123)  ## Don't change this line. It makes the result reproducible.
# Your code here (use `while`)

set.seed(123)  ## Don't change this line. It makes the result reproducible.
# Your code here (use `repeat`)

Part 2. Apply Operations (2+5 pts)

1. Create a vector a that contains all the even numbers ranging from -4 to 10. Compute the cosine value of each entry using the sapply() function.

# Your code here

2. Run the code below to obtain a list of results. Here, lm() function is used to run a linear regression.

linearMod = lm(dist ~ speed, data = cars) 

• What are the names of the elements in the list linearMod?

• Compute the mean and variance of each column of the model element in the list linearMod using apply() function.

• Compute the length of each element in the list linearMod. How many of them have length 2?

# Your code starts from here

Part 3. More Data Frames and Apply (4+3+2+3+2+4 pts)

We will examine data from the 2016 Summer Olympics in Rio de Janeiro, originally taken from https://github.com/flother/rio2016. Below, we read in the data and store it as rio. All the following questions will be answered based on rio.

rio = 
  read.csv(url("https://github.com/zhangyk8/zhangyk8.github.io/raw/master/_teaching/file_stat302/Data/rio.csv"), 
           header = TRUE)

1. What kind of object is rio? What are its dimensions and columns names of rio? Is there any missing data (i.e., NA)?

• Answer in words: What does each row represent?

# Your code starts from here

2. How many athletes competed the 2016 Summer Olympics? How many countries were represented? How many athletes had duplicate name? (Hint: Look at the function duplicated().)

# Your code starts from here

3. Which country brought the most athletes, and how many was this? (Hint: for a factor variable f, you can use table(f) to see how many elements in f are in each level of the factor.)

# Your code starts from here

4. How many medals of each type – gold, silver, bronze – were awarded at this Olympics? Are they equal? (Output the logical TRUE/FALSE.)

• Answer in words: Is this result surprising, and can you explain what you are seeing?

# Your code starts from here

5. Create another column called total in the data frame rio which adds the number of gold, silver, and bronze medals for each athlete. Which athlete had the most number of medals?

# Your code starts from here

6. Using tapply(), calculate the total medal count for each country. Save the result as tot_nat. Which country had the most number of medals, and how many was this? How many countries had zero medals?

# Your code starts from here