(require (lib "list.ss"))

(define eventspace list)

(define (size-of eventspace) (length eventspace))

; assumes uniform eventspace
(define (P event eventspace)
  (if (member event eventspace)
      (/ 1 (size-of eventspace))
      0))
  

(define (die-roll event) event)

(define (expected-value rv eventspace)
  (foldr (lambda (e r) (+ (* (rv e) (P e eventspace)) r)) 0 eventspace))

(define (moment rv n eventspace)
  (expected-value (lambda (event) (expt (rv event) n)) eventspace))

(define (central-moment rv n eventspace)
  (let ((rv-expectation (expected-value rv eventspace)))
    (expected-value (lambda (e) (expt (- (rv e) rv-expectation) n)) eventspace)))

(define (variance rv eventspace)
  (central-moment rv 2 eventspace))

(define (standard-deviation rv eventspace)
  (sqrt (variance rv eventspace)))