Problem Set 9
CIS 166 & CMP 230, Introductory Programming
Lehman College, City University of New York
Fall 2012

Due Date: midnight, Friday, 6 December.

This assignment focuses on design and simulation from Chapter 9.

Submit the following programs via Blackboard:

1. Modify the stock simulation from Lab 10 to calculate and print the average ending value of money.


2. Is it likely that a monkey at a typewriter, randomly choosing character, could write Hamlet?

   Write a simulation to answer this question. That is, write a program that will randomly generate 100,000 strings of length 5 and count the number of strings that match "to be". You may assume that your strings are lower case letters and spaces only. That is, when you generate your string, you are choosing from the 27 characters: [' ','a','b','c','d',...'y','z']

3. A bellwether state is one that has voted with the winner over past elections. For example, both Ohio and Nevada have voted for the presidential winner in all the elections since 1980.

   Write a function to simulate the voting of the 50 states. Your function should take as input the number of elections to simulate, and then simulate the elections in the 50 states, assuming that each has 50% probability of voting for the winner.

   In your main() function in your program, you should call your function 1000 times with the input parameter values: 1, 2, 3, 4, 5, and 10, and print out the number of bellweather states you would expect for each number of elections. That is, your output should look like:

   	    Number of Elections      Number of Bellweather states
   	    1                        your calculation goes here!
   	    2                        your calculation goes here!
   	    3                        your calculation goes here!
   	    4                        your calculation goes here!
   	    5                        your calculation goes here!
   	    9                        your calculation goes here! 
   	    10                       your calculation goes here!
   	 

4. Chapter 9, #13 (random walk) - Suppose you are doing a random walk on the blocks of a city. At each "step" you choose to walk one block (at random) either forward, backward, left or right. In n steps, how far do you expect to be from your starting point? Write a program to help answer this question.


5. Chapter 9, #14 (graphical random walk) - Write a graphical random walk in two dimensions. In this simulation you should allow the step to be taken in any direction. You can generate a random direction an an angle off the x axis.

   angle = random() * 2 * math.pi

   The new x and y positions are then given by these formulas:

   • x = x + cos(angle)
   • y = y + sin(angle)

   The program should take the number of steps as an input. Start your walker at the center of a 100x100 grid and draw a line that traces the walk as it progresses.

For more information on using Blackboard, see the first lab.

General Notes

• Two of the five submitted programs will be chosen at random for grading.
• Assignments must be submitted by midnight on the date due.
• Every program should begin with a comment that includes your name and a brief description.
• No credit will be given for a late assignment.
• Extra credit will be awarded for graded programs that are submitted early. If a graded program is submitted more than 12 hours early (before Friday noon), 1 extra credit point will be awarded. For graded programs submitted more than 24 hours early (Thursday or earlier), 2 extra credit points will be awarded.
• You MUST attach your program as a file, you may also cut and paste your program into the submission box.
• The name of the file that you submit should begin with your last name (for example: yourlastnamePS2_2.py). Your file MUST have a file type of .py
• Your program should contain a function definition for main(), and it should invoke main() at the end of the program.
• While working on this assignment you have access to help in class (if your question might be of general interest), at the Math Lab, during office hours, and using the discussion forum for this problem set on Blackboard. Please take advantage of all of these resources.