Random Number Generators

Exercise 1

Run each of the following examples within Scheme several times

For example, you might enter (random 6) into the computer ten times.

Describe what results.

Exercise 2

Type (random 1). Why do you think the result always is 0?

Exercise 3

What happens if you type (random -5)?

Exercise 4

The following procedure simulates the roll of a die:

   (define roll-a-die 
      (lambda ()             ;;; (random 6) gives integers 0,1,2,3,4,5
          (+ 1 (random 6))   ;;; so add 1 to get integers  1,2,3,4,5,6
      )
   )

Enter the definition of roll-a-die into Scheme. Confirm that roll-a-die works correctly by typing (roll-a-die) several times.

Exercise 5

Explain why the parentheses are needed when running the roll-a-die procedure.
(Consider, for example, what happens if roll-a-die is typed without the parentheses.)

Exercise 6

To roll a die n times, we could construct a list with each result of calling the roll-a-die procedure. A parameter n allows us to count the number of rolls left to go.

   (define roll
      (lambda (n)
         (if (<= n 0)
             '()          ;;; rolling a die 0 times gives null list
             (cons (roll-a-die) (roll (- n 1))))  
                          ;;; add current roll to list of rest
      )
   )

Enter the definition of roll into Scheme, and check that it works correctly.
Explain in a few sentences why roll simulates the rolling of a die.

What happens if you call (roll 10) several times?
Do you get the same list of 10 die rolls each time?

Exercise 7

Modify your previous work to obtain a procedure count-2s, which counts the number of 2's rolled when a die is thrown n times.

Exercise 8

We can simulate the tossing of a coin by generating real numbers between 0 and 1 and then considering a "head" to correspond to a number less than 0.5.

Write a procedure coin which simulates the flipping of a coin.
(coin should return either the string "head" or the string "tail".)

This document is available on the World Wide Web as

http://www.math.grin.edu/~walker/courses/151.sp04/labs/random-numbers.xhtml

created February 5, 1997 last revised January 16, 2004
For more information, please contact Henry M. Walker at walker@cs.grinnell.edu.