#light
open System

//random number generator with 6 numbers
let ran = new Random()
let random5() = ran.Next(5)

//naive
let rantbl = [| 0 .. 6 |]               
let rec random7() = let i,j = random5(), random5()                   
                    let sum = i + j
                    if  sum < rantbl.Length then randomTable.[sum]
                    else random7()

let randomTable = [|for i in 0 .. 24 do if i / 7<3 then yield i % 7 
                                        else yield -1 |] 
let rec random7_2() = let i,j = random5(), random5()                  
                      let index = i  * 5 + j
                      if  randomTable.[index] <> -1 then randomTable.[index]
                      else random7_2()

let sampler sample = seq { for i in 0 .. 100000 do yield sample() }                     
                                 
let variance sample N =  let mean = sample |> Seq.average_by (fun i-> float i)
                         (sample |> Seq.sum_by (fun i->(float i - mean) * (float i - mean) ))
                                                     / N                                                       
let standardDeviation varian= sqrt (varian)
                      
let standardError sample =  let N = float (Seq.length sample)
                            let vari = variance sample N
                            let stDev = standardDeviation vari
                            stDev / (sqrt N)
                           

let sample = sampler random7
standardError(sampler random7 )
standardError (sampler random7_2)

// uniform distribution
let errorSet mySet = let N = Seq.length mySet |> float
                     mySet |> Seq.count_by (fun e-> e)  |> Seq.map (fun (i,j) -> i, (float j)/N * 100.0) |> Map.of_seq
                     
errorSet (sampler random7)                     
errorSet (sampler random7_2)                     
                    
print5                     
random7()