Create two c++ programs for each problem. Every rule and instructions are included in the file.

Problem A: Flipping a Fair Coin

Write a C++ program that simulates flipping a fair coin. Your program should do the following:

Problem B: Variation on the Coin Flipping

Repeat the process in Problem A except make the following changes:

hw03 (1).pdf

CSci 1113: Introduction to C/C++
Programming for Scientists and Engineers
Homework 03: Loops and Random Numbers
Spring 2017
Due Date: Friday, Feb. 24, 2015; 6:00pm.
Purpose:
This homework involves some further basics of C++ programming, specifically loops. You will also get
to work with random numbers, which are important in scientific simulations.
Instructions:
The instructions are similar to the previous homework: this is an individual, not collaborative
assignment; remember to be careful with naming rules; etc. See the HW 0 description for more details.
Problem Introduction:
Probabilistic simulations are an important computational tool used in a variety of areas. Suppose we
have a random process and take N random samples for some positive integer N. Then we take a N more
random samples of the same process. How close do we expect the average of the first sets of samples to
be to the second set of samples? For example, if the random numbers are from a uniform distribution
between 0 and 100, what is that chance that the average of 100 random samples differs by more than
3.0 from the average of the next 100 random samples?
Researchers who study probability have derived some powerful theoretical results about questions like
these. But another (less rigorous but still useful) way to study such questions is though computational
simulations. This homework asks you to write some C++ programs that simulate sets of random
samples.
Problem A: Flipping a Fair Coin
Write a C++ program that simulates flipping a fair coin. Your program should do the following:
1. Ask the user to input a random seed (of type int), and call srand with that input number as its
argument. That is, right after the variable declarations in your program you should have the
lines:
cout << "Input the random seed: ";
cin >> seed;
srand(seed);
2. Ask the user to input a difference value d, which should be an int.
3. Uses the cmath function rand() to generate a random number that is either 0 or 1. A 0
corresponds to a tail, and 1 to a head, and both possibilities should be equally likely. Repeat this
process 100 times, counting the number of heads. Note that rand() generates double-type
random numbers from 0 to 1 (inclusive), with all numbers being equally probable. Your task is
to convert the generated number to 0 or 1, maintaining the equally probable property.
4. Repeat Step 3 (i.e., generate another 100 random numbers) and count the number of heads in
those 100 flips. 5. If the differences in the counts from Steps 3 and 4 is greater than or equal to the user input
difference d, then stop. Otherwise repeat Steps 3 and 4 and check if the difference of the counts
of these new samples is greater than or equal to d. If it is, stop. Continue this process until the
difference in the counts is greater than or equal to d, or Steps 3 and 4 have been repeated 8
times.
Here is an example run:
Input the random seed: 346
Input the difference: 8
Set 1 Set 2 1 54 56 2 46 49 3 51 52 4 45 48 5 55 41 Test your program a variety of times to make sure its answers are correct, as best you can tell. When
you have written, tested, and corrected your solution, save your file as <username>_3A.cpp, where you
replace <username> with your U of M username. Submission information is given after Problem B. As
usual, be diligent in following this naming convention.
Problem B: Variation on the Coin Flipping
Repeat the process in Problem A except make the following changes:
1. The user input difference d should be a double rather than an int.
2. Instead of generating a 0 or a 1 each time, generate a random number that is a double in the
range [40.0, 100.0]. Each number in this range should be equally likely.
3. Print the averages with 2 digits to the right of the decimal point.
4. Instead of the stopping criterion in Problem A, always run 10 repetitions. However, after all 10
are completed, print out how many of them had their averages differ by more than the user input
difference d.
5. The entire process (after setting the random seed) should be in a do - while continuation loop.
So the program should always run the 10 repetitions mentioned in Step 4. Then the program
should ask the user if they wish to repeat the process. If the user inputs a ‘y’ or ‘Y’, then the
program should repeat this process. The program should continue in this vein until the user
enters a character other than ’y’ or ’Y’.
Other than these changes, your Problem B program should be the same as Problem A. (Hint: copy and
modify your Problem A solution rather than writing this part from scratch. However, make sure you
save your Problem A solution and in this part work with the copy.)
(Continues next page) Here is an example of running the program:
Input the random seed: 346
Input the difference: 3.5
Set 1 Set 2 1 70.76 66.28 2 69.93 69.29 3 71.05 70.03 4 74.08 71.96 5 68.21 66.04 6 73.45 67.48 7 68.62 69.44 8 70.21 67.22 9 67.82 67.51 10 72.87 70.97 Number that exceeded 3.50: 2
Repeat the process (y/n)? y
Input the difference: 4.2
Set 1 Set 2 1 70.73 65.68 2 69.80 71.54 3 70.65 68.06 4 68.30 70.36 5 68.83 70.35 6 70.94 68.92 7 71.29 73.50 8 66.92 68.72 9 69.97 70.17 10 67.99 68.70 Number that exceeded 4.20: 1
Repeat the process (y/n)? n
Test your program a variety of times to make sure its answers are correct, as best you can tell. When
you have written, tested, and corrected your solution, save your file as <username>_3B.cpp, where you
replace <username> with your U of M username, and submit it together with the Problem A source file using the Homework 3 link in Moodle. As usual, be diligent in following this naming convention.
Please note, both files must be uploaded separately in Moodle, and you can only upload at most two
files.

Attachments:

• 1493692424-hw03 1.pdf