The preceding histogram looks a great deal like a normal distribution, but in fact it is a binomial distribution. The two distributions are very similar, but the binomial distribution is used to model cases where we want to determine how many times a binary event is expected to occur.
Let's plot both the binomial and the normal distribution on a histogram to see how they compare:
(defn ex-4-9 []
(let [passengers (concat (repeat 127 0)
(repeat 339 1))
bootstrap (s/bootstrap passengers i/sum :size 10000)
binomial (fn [x]
(s/pdf-binomial x :size 466 :prob (/ 339 466)))
normal (fn [x]
(s/pdf-normal x :mean 339 :sd 9.57))]
(-> (c/histogram bootstrap
:x-label "Female Survivors"
:series-label "Bootstrap"
:nbins 20
:density true
:legend true)
(c/add-function binomial...