STAT 385 Lab 02

We will continue working with the deck of cards example we have seen in lectures. First, let’s load the dataset to RStudio.

Exercise 1: King of Hearts

Load data

• Load the dataset and store the data in a data frame called deck.
• The dataset cards.csv is available at URL: https://nkha149.github.io/stat385-sp2020/files/data/cards.csv.

Modifying the deck

• We will modify the deck for a game called “King of Hearts” where:
  • All kings get the highest value, 14 in the deck.
  • All cards in the hearts suit get the value of 10 (except the king of hearts, its value should be 14).

Use the following code to check your new deck:

deck[deck$suit == "hearts", ]

##     face   suit value
## 40  king hearts    14
## 41 queen hearts    10
## 42  jack hearts    10
## 43   ten hearts    10
## 44  nine hearts    10
## 45 eight hearts    10
## 46 seven hearts    10
## 47   six hearts    10
## 48  five hearts    10
## 49  four hearts    10
## 50 three hearts    10
## 51   two hearts    10
## 52   ace hearts    10

deck[deck$face == "king", ]

##    face     suit value
## 1  king   spades    14
## 14 king    clubs    14
## 27 king diamonds    14
## 40 king   hearts    14

Adding the jackpot column

• Now, create a new column called jackpot in the data frame deck.
  • jackpot takes value of TRUE and FALSE.
  • For the king of hearts, the value of jackpot is TRUE.
  • For all other rows, the value of jackpot is FALSE.

Your deck should look like this after modifying the value.

deck

##     face     suit value jackpot
## 1   king   spades    14   FALSE
## 2  queen   spades    12   FALSE
## 3   jack   spades    11   FALSE
## 4    ten   spades    10   FALSE
## 5   nine   spades     9   FALSE
## 6  eight   spades     8   FALSE
## 7  seven   spades     7   FALSE
## 8    six   spades     6   FALSE
## 9   five   spades     5   FALSE
## 10  four   spades     4   FALSE
## 11 three   spades     3   FALSE
## 12   two   spades     2   FALSE
## 13   ace   spades     1   FALSE
## 14  king    clubs    14   FALSE
## 15 queen    clubs    12   FALSE
## 16  jack    clubs    11   FALSE
## 17   ten    clubs    10   FALSE
## 18  nine    clubs     9   FALSE
## 19 eight    clubs     8   FALSE
## 20 seven    clubs     7   FALSE
## 21   six    clubs     6   FALSE
## 22  five    clubs     5   FALSE
## 23  four    clubs     4   FALSE
## 24 three    clubs     3   FALSE
## 25   two    clubs     2   FALSE
## 26   ace    clubs     1   FALSE
## 27  king diamonds    14   FALSE
## 28 queen diamonds    12   FALSE
## 29  jack diamonds    11   FALSE
## 30   ten diamonds    10   FALSE
## 31  nine diamonds     9   FALSE
## 32 eight diamonds     8   FALSE
## 33 seven diamonds     7   FALSE
## 34   six diamonds     6   FALSE
## 35  five diamonds     5   FALSE
## 36  four diamonds     4   FALSE
## 37 three diamonds     3   FALSE
## 38   two diamonds     2   FALSE
## 39   ace diamonds     1   FALSE
## 40  king   hearts    14    TRUE
## 41 queen   hearts    10   FALSE
## 42  jack   hearts    10   FALSE
## 43   ten   hearts    10   FALSE
## 44  nine   hearts    10   FALSE
## 45 eight   hearts    10   FALSE
## 46 seven   hearts    10   FALSE
## 47   six   hearts    10   FALSE
## 48  five   hearts    10   FALSE
## 49  four   hearts    10   FALSE
## 50 three   hearts    10   FALSE
## 51   two   hearts    10   FALSE
## 52   ace   hearts    10   FALSE

Function draw()

• Write a function draw() that randomly draws 4 cards from the deck WITHOUT replacement and compute the sum of the 4 cards that were drawn.
  • Input: no input provided.
  • Output: a number representing the sum of values of the 4 cards drawn.

Use the following code to test your function:

set.seed(385)
draw()

## [1] 22

set.seed(420)
draw()

## [1] 36

set.seed(400)
draw()

## [1] 29

set.seed(2020)
draw()

## [1] 31

Function win_jackpot()

• This is a strange game where a person can win a jackpot through 3 possible ways:
  • Getting a king of hearts in the 4 cards drawn.
  • OR getting 4 cards from the same suit.
  • OR getting 4 cards with the same face.
• Write a function win_jackpot() that:
  • randomly draws 4 cards from the deck WITHOUT replacement
  • print out the 4 cards using the print() function
  • and returns TRUE if the 4 cards drawn satisfying one of the above conditions, FALSE otherwise.
• Hint: You might want to take a look at the unique() function to test the 2nd and 3rd conditions.

set.seed(385)
win_jackpot()

##     face   suit value jackpot
## 6  eight spades     8   FALSE
## 26   ace  clubs     1   FALSE
## 23  four  clubs     4   FALSE
## 18  nine  clubs     9   FALSE

## [1] FALSE

set.seed(35)
win_jackpot()

##     face   suit value jackpot
## 10  four spades     4   FALSE
## 6  eight spades     8   FALSE
## 8    six spades     6   FALSE
## 1   king spades    14   FALSE

## [1] TRUE

set.seed(174)
win_jackpot()

##    face   suit value jackpot
## 22 five  clubs     5   FALSE
## 1  king spades    14   FALSE
## 48 five hearts    10   FALSE
## 40 king hearts    14    TRUE

## [1] TRUE

set.seed(2260)
win_jackpot()

##    face     suit value jackpot
## 13  ace   spades     1   FALSE
## 52  ace   hearts    10   FALSE
## 39  ace diamonds     1   FALSE
## 26  ace    clubs     1   FALSE

## [1] TRUE

Running simulation on win_jackpot()

Now, we want to estimate the probability of winning the jackpot in “King of Hearts”. How do we do that? We can do so using simulation studies, that is running the win_jackpot() function many many times and record the number of times we win. In this example, the number of simulations is 10000.

<!!!>BEWARE<!!!>: You need to change your win_jackpot() function before progressing to the next part.

• First, write a new function called win_jackpot2():
  • Copy the code from your original win_jackpot() function.
  • Remove the print() statement from the code.
  • Test your win_jackpot2() function:

set.seed(174)
win_jackpot2()

## [1] TRUE

• Use the following code to run the simulation studies:
  • Make sure you copy and paste! If you retype the code, remember win_jackpot2()!!! Missing the 2 will cost you heavily!

results <- replicate(win_jackpot2(), n = 5000)

• Now, use results to compute the estimated probability of winning a jackpot. Your answer should be 0.0886.

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Exercise 2: 2015 Flight Delays and Cancellations Data

Next, we take a quick look at the 2015 Flight Delays and Cancellations Data provided by the U.S. Department of Transportation. This is a huge dataset availalbe on Kaggle. But for us, we will only take a look at flights flying out from O’Hare International Airport (ORD) in January, 2015.

Load data

• I have filtered out the data specific to O’Hare and stored it in ohare_jan.csv. You can TRY load the data from the following URL: https://nkha149.github.io/stat385-sp2020/files/data/ohare_jan.csv.
  • You probably will get an error!
  • What do you do?
  • Try downloading the file and load the data through the RStudio interface instead!
• Save the data into a data frame named flights.

Counting

• Count how many flights departed from ORD in January, 2015.
  • Your answer should be 23484.
• Count how many flights departed from ORD that were American Airlines flights (AA) in January, 2015.
  • Your answer should be 3899.
• Look at function table(). Use it to get a summary of the number of flights flying out from ORD for each airline in January, 2015.
  • Your result should look as followed:

## 
##   AA   AS   B6   DL   EV   F9   MQ   NK   OO   UA   US   VX 
## 3899  100  170  569 3767  283 5655  767 3181 4383  634   76