The binomial distribution

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...