Teorver task1

area.hs

import Data.Functor
import System.Random
import System.Random.Mersenne.Pure64
import Text.Printf

import Statistics.Distribution (quantile)
import Statistics.Distribution.Normal
import Statistics.Distribution.Uniform


gamma = 0.98
k = 6
c = 13.8
a = 4
f = (a**)
fF = sum . map f

main = do
    -- Хороший генератор случайных чисел (вихрь Мерсенна)
    gen <- newPureMT

    let n = 10^4
        points = take n $ randomPoints gen
        vals = fF <$> points
        s = (fromIntegral . length $ filter (<= c) vals) / (fromIntegral n)                         -- <- вероятность попадания (она же искомая площадь)
        interval = (quantile standard ((gamma+1) / 2)) * (sqrt $ s*(1-s)) / (sqrt $ fromIntegral n) -- <- доверительный интервал

    putStrLn $ printf "n = %d: %.4f ± %.4f (%.2f%%)" n s interval (interval/s * 100)

randomPoints :: RandomGen g => g -> [[Double]]
randomPoints gen = splitList $ randomRs (0, 1) gen
    where splitList l = let (v, r) = splitAt k l in v : splitList r