library$($tidyverse$)$ #data manipulation & plotting

library$($stringr$)$ # text cleaning and regular expressions

library$($tidytext$)$ # provides additional text mining functions

LOTR readRDS$("$LOTR$.$RDS$")$ ## read in the text of

stop$\_$words tidytext::stop$\_$words

tokens LOTR $\%>\%$ unnest$\_$tokens $($word$,$ text$)$

tokens tokens $\%>$ dplyr::filter$(!$word $\%$in$\%$ stop$\_$words $ word $)$

all$\_$word$\_$counts tokens $\%>\%$ group$\_$by$($book$,$ chapter$)\%>\%$

count $($word$,$ sort $=$ TRUE$)\%>\%$ ungroup

all$\_$word$\_$counts$\_$mat all$\_$word$\_$counts $\%\%$ spread $($key$=$word, value$=$n$,$ fill$=0)$

word$\_$counts all$\_$word$\_$counts$\_$mat $[["$ring$"]]$

Plot the log$-$likelihood of the Poisson rate of usage of the word in word$\_$counts. Then use word$\_$counts

to compute the maximum likelihood estimate of the rate of the usage of the word in the LOTR. Mark

this maximum on the log$-$likelihood plot with a vertical line $($use abline if you make the plot in base $R$ or

geom$\_$vline if you prefer ggplot$).$