Step by Step solution about How to resolve the algorithm Statistics/Normal distribution step by step in the Go programming language

The provided Go program simulates a normal (Gaussian) distribution and presents the results both numerically and graphically. Here's a breakdown of the code:

1. Header and Imports:

   • The code starts with the package main declaration.
   • It imports several standard Go libraries:
     • "fmt" for input and output
     • "math" for mathematical functions
     • "math/rand" for generating random numbers
     • "strings" for string manipulation

2. Constants:

   • n: The number of random numbers to generate (10,000 in this case).
   • bins: The number of bins in the histogram (12).
   • sig: The standard deviation of the normal distribution (3).
   • scale: A scaling factor for the histogram (100).

3. norm2 Function:

   • This function implements the Box-Muller transform to generate a pair of normally distributed random numbers with zero mean and unit variance.

4. main Function:

   • sum, sumSq: Variables to calculate the sum and sum of squares of the generated numbers.
   • h: An array of integers to store the histogram counts.
   • accum: A function that takes a float64 value and updates the sum, sumSq, and histogram count.
   • The main loop generates n/2 pairs of normally distributed random numbers using norm2. Each pair is passed to the accum function, which keeps track of the sum, sum of squares, and adds to the histogram count for the corresponding bin.

5. Printing Results:

   • The mean and standard deviation of the generated numbers are calculated and printed.
   • A histogram is built using asterisks (*) to represent the count in each bin. The height of each histogram bar is scaled down by scale for a more manageable display.

package main

import (
    "fmt"
    "math"
    "math/rand"
    "strings"
)

// Box-Muller
func norm2() (s, c float64) {
    r := math.Sqrt(-2 * math.Log(rand.Float64()))
    s, c = math.Sincos(2 * math.Pi * rand.Float64())
    return s * r, c * r
}

func main() {
    const (
        n     = 10000
        bins  = 12
        sig   = 3
        scale = 100
    )
    var sum, sumSq float64
    h := make([]int, bins)
    for i, accum := 0, func(v float64) {
        sum += v
        sumSq += v * v
        b := int((v + sig) * bins / sig / 2)
        if b >= 0 && b < bins {
            h[b]++
        }
    }; i < n/2; i++ {
        v1, v2 := norm2()
        accum(v1)
        accum(v2)
    }
    m := sum / n
    fmt.Println("mean:", m)
    fmt.Println("stddev:", math.Sqrt(sumSq/float64(n)-m*m))
    for _, p := range h {
        fmt.Println(strings.Repeat("*", p/scale))
    }
}