; How do I compute the sum of N random numbers?


;;; Procedure:
;;;   sum-n-random
;;; Parameters:
;;;   n, an integer (the number of random integers)
;;;   low, the lower bound of the range of random integer
;;;   high, the upper bound of the range of random integer
;;; Purpose:
;;;   To compute the sum of n random integers in the range
;;;   [low..high] (inclusive).
;;; Produces:
;;;   sum, an integer
;;; Preconditions:
;;;   low <= high
;;;   n is not negative
;;; Postconditions:
;;;   sum = r1 + r2 + ... + rn
;;;     where ri in [low..high] for all i between 1 and n.
;;;   sum is hard to predict.  (In particular, it will be different
;;;     for different calls of sum-n-random and the results of
;;;     subsequent calls will not follow an easy-to-detect pattern.)
;;;   sum follows the appropriate statistical distribution for a
;;;     sum in which each ri is also difficult to predict.
(define sum-n-random
  (lambda (n low high)
    (if (= n 0)
        0
        (+ (ranged-random low high)
           (sum-n-random (- n 1) low high)))))

(define sum-n-random-wrong
  (lambda (n low high)
    (ranged-random (* n low) (* n high))))

; Side note: (random x) returns a hard-to-predict integer in the
; range [0..x).
; How do you produce a number in the range [low..high]
; (+ low (random (- high low)))
(define ranged-random
  (lambda (low high)
    (+ low (random (+ 1(- high low))))))

(define random-list
  (lambda (length low high)
    (if (= length 0) null
        (cons (ranged-random low high)
              (random-list (- length 1) low high)))))

(define random-sums
  (lambda (length n low high)
    (let kernel ((to-go length))
      (if (= to-go 0) null
          (cons (sum-n-random n low high)
                (kernel (- to-go 1)))))))