---
title: "Lab 3: Programming Fundamentals"
author: "INSERT YOUR NAME HERE (INSERT YOUR UW NETID HERE)"
date: "Due by 23:59pm on Jan 30, 2024"
output:
  pdf_document: default
  html_document: default
---

### 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`).

```{r}
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`.)


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


```{r}
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.

```{r}
# Your code here
```

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

```{r}
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?

```{r}
# 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](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`.

```{r}
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?

```{r}
# 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()`.) 

```{r}
# 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.)

```{r}
# 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?

```{r}
# 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? 

```{r}
# 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?

```{r}
# Your code starts from here
```