The flights data set seen in class is available in the package nycflights$13$ as a tibble. It contains on$-$time

data for all flights that departed New York City via its three main airports throughout the whole year of

$2013.$ The airport from which each flight departed is recorded in the origin column.

a$)$ Load the tidyverse suite of packages, as well as the nycflights$13$ package and the flights data

therein.

b$)$ Cancelled flights are defined as those for which no departure or arrival took place. Write code using

pipe operators and filter$()$ to create a new data set flights$2$ which removes any rows with missing

values $($i$.$e$.$ NA entries$)$ for the dep$\_$delay or arr$\_$delay variables $($Hint: see $?$is$.$na and use the "and"

operator & and the negation operator $!).$

c$)$ Define the new variable gain as the difference between the departure delay and the arrival delay, the

new variable air$\_$hour as the air$\_$time variable re$-$expressed in hours, and the variable gain$\_$per$\_$hour

as the gain per air$\_$hour. Write code using pipe operators and the functions mutate$()$ and select$()$

which creates a new tibble called flights$3$ containing only the gain$\_$per$\_$hour and origin variables.

$($Hint: you may exploit the fact that mutate$()$ allows you to refer to variables you have just created$).$

d$)$ The ggplot$2$ code below plots a kernel density estimate of the gain$\_$per$\_$hour for each origin airport.

However, it overplots all three estimated density curves on the one graph. Modify this code so that it

$($i$)$ partitions$/$facets the graph into a separate panel for each origin and $($ii$)$ produces histograms with

$50$ bins rather than density plots.