Home > Articles

Functions and Modules

This chapter is from the book


  • 2.2.1 Add to Gaussian (PROGRAM 2.1.2) an implementation of the three-argument static method pdf(x, mu, sigma) specified in the API that computes the Gaussian probability density function with a given mean μ and standard deviation σ, based on the formula ϕ(x, μ, σ) = ϕ(( x– μ) / σ)/σ. Also add an implementation of the associated cumulative distribution function cdf(z, mu, sigma), based on the formula Φ(z, μ, σ) = Φ((z – μ) / σ).

  • 2.2.2 Write a library of static methods that implements the hyperbolic functions based on the definitions sinh(x) = (exex) / 2 and cosh(x) = (ex + ex) / 2, with tanh(x), coth(x), sech(x), and csch(x) defined in a manner analogous to standard trigonometric functions.

  • 2.2.3 Write a test client for both StdStats and StdRandom that checks that the methods in both libraries operate as expected. Take a command-line argument n, generate n random numbers using each of the methods in StdRandom, and print their statistics. Extra credit: Defend the results that you get by comparing them to those that are to be expected from analysis.

  • 2.2.4 Add to StdRandom a method shuffle() that takes an array of double values as argument and rearranges them in random order. Implement a test client that checks that each permutation of the array is produced about the same number of times. Add overloaded methods that take arrays of integers and strings.

  • 2.2.5 Develop a client that does stress testing for StdRandom. Pay particular attention to discrete(). For example, do the probabilities sum to 1?

  • 2.2.6 Write a static method that takes double values ymin and ymax (with ymin strictly less than ymax), and a double array a[] as arguments and uses the StdStats library to linearly scale the values in a[] so that they are all between ymin and ymax.

  • 2.2.7 Write a Gaussian and StdStats client that explores the effects of changing the mean and standard deviation for the Gaussian probability density function. Create one plot with the Gaussian distributions having a fixed mean and various standard deviations and another with Gaussian distributions having a fixed standard deviation and various means.

  • 2.2.8 Add a method exp() to StdRandom that takes an argument λ and returns a random number drawn from the exponential distribution with rate λ. Hint: If x is a random number uniformly distributed between 0 and 1, then –ln x / λ is a random number from the exponential distribution with rate λ.

  • 2.2.9 Add to StdRandom a static method maxwellBoltzmann() that returns a random value drawn from a Maxwell–Boltzmann distribution with parameter σ. To produce such a value, return the square root of the sum of the squares of three random numbers drawn from the Gaussian distribution with mean 0 and standard deviation σ. The speeds of molecules in an ideal gas obey a Maxwell–Boltzmann distribution.

  • 2.2.10 Modify Bernoulli (PROGRAM 2.2.6) to animate the bar graph, replotting it after each experiment, so that you can watch it converge to the Gaussian distribution. Then add a command-line argument and an overloaded binomial() implementation to allow you to specify the probability p that a biased coin comes up heads, and run experiments to get a feeling for the distribution corresponding to a biased coin. Be sure to try values of p that are close to 0 and close to 1.

  • 2.2.11 Develop a full implementation of StdArrayIO (implement all 12 methods indicated in the API).

  • 2.2.12 Write a library Matrix that implements the following API:

    public class Matrix
    double dot(double[] a, double[] b)

    vector dot product

    double[][] multiply(double[][] a, double[][] b)

    matrix-matrix product

    double[][] transpose(double[][] a)


    double[] multiply(double[][] a, double[] x)

    matrix-vector product

    double[] multiply(double[] x, double[][] a)

    vector-matrix product

    (See SECTION 1.4.) As a test client, use the following code, which performs the same calculation as Markov (PROGRAM 1.6.3):

    public static void main(String[] args)
       int trials = Integer.parseInt(args[0]);
       double[][] p = StdArrayIO.readDouble2D();
       double[] ranks = new double[p.length];
       rank[0] = 1.0;
       for (int t = 0; t < trials; t++)
           ranks = Matrix.multiply(ranks, p);

    Mathematicians and scientists use mature libraries or special-purpose matrix-processing languages for such tasks. See the booksite for details on using such libraries.

  • 2.2.13 Write a Matrix client that implements the version of Markov described in SECTION 1.6 but is based on squaring the matrix, instead of iterating the vector–matrix multiplication.

  • 2.2.14 Rewrite RandomSurfer (PROGRAM 1.6.2) using the StdArrayIO and StdRandom libraries.

    Partial solution.

    double[][] p = StdArrayIO.readDouble2D();
    int page = 0; // Start at page 0.
    int[] freq = new int[n];
    for (int t = 0; t < trials; t++)
       page = StdRandom.discrete(p[page]);

InformIT Promotional Mailings & Special Offers

I would like to receive exclusive offers and hear about products from InformIT and its family of brands. I can unsubscribe at any time.


Pearson Education, Inc., 221 River Street, Hoboken, New Jersey 07030, (Pearson) presents this site to provide information about products and services that can be purchased through this site.

This privacy notice provides an overview of our commitment to privacy and describes how we collect, protect, use and share personal information collected through this site. Please note that other Pearson websites and online products and services have their own separate privacy policies.

Collection and Use of Information

To conduct business and deliver products and services, Pearson collects and uses personal information in several ways in connection with this site, including:

Questions and Inquiries

For inquiries and questions, we collect the inquiry or question, together with name, contact details (email address, phone number and mailing address) and any other additional information voluntarily submitted to us through a Contact Us form or an email. We use this information to address the inquiry and respond to the question.

Online Store

For orders and purchases placed through our online store on this site, we collect order details, name, institution name and address (if applicable), email address, phone number, shipping and billing addresses, credit/debit card information, shipping options and any instructions. We use this information to complete transactions, fulfill orders, communicate with individuals placing orders or visiting the online store, and for related purposes.


Pearson may offer opportunities to provide feedback or participate in surveys, including surveys evaluating Pearson products, services or sites. Participation is voluntary. Pearson collects information requested in the survey questions and uses the information to evaluate, support, maintain and improve products, services or sites, develop new products and services, conduct educational research and for other purposes specified in the survey.

Contests and Drawings

Occasionally, we may sponsor a contest or drawing. Participation is optional. Pearson collects name, contact information and other information specified on the entry form for the contest or drawing to conduct the contest or drawing. Pearson may collect additional personal information from the winners of a contest or drawing in order to award the prize and for tax reporting purposes, as required by law.


If you have elected to receive email newsletters or promotional mailings and special offers but want to unsubscribe, simply email information@informit.com.

Service Announcements

On rare occasions it is necessary to send out a strictly service related announcement. For instance, if our service is temporarily suspended for maintenance we might send users an email. Generally, users may not opt-out of these communications, though they can deactivate their account information. However, these communications are not promotional in nature.

Customer Service

We communicate with users on a regular basis to provide requested services and in regard to issues relating to their account we reply via email or phone in accordance with the users' wishes when a user submits their information through our Contact Us form.

Other Collection and Use of Information

Application and System Logs

Pearson automatically collects log data to help ensure the delivery, availability and security of this site. Log data may include technical information about how a user or visitor connected to this site, such as browser type, type of computer/device, operating system, internet service provider and IP address. We use this information for support purposes and to monitor the health of the site, identify problems, improve service, detect unauthorized access and fraudulent activity, prevent and respond to security incidents and appropriately scale computing resources.

Web Analytics

Pearson may use third party web trend analytical services, including Google Analytics, to collect visitor information, such as IP addresses, browser types, referring pages, pages visited and time spent on a particular site. While these analytical services collect and report information on an anonymous basis, they may use cookies to gather web trend information. The information gathered may enable Pearson (but not the third party web trend services) to link information with application and system log data. Pearson uses this information for system administration and to identify problems, improve service, detect unauthorized access and fraudulent activity, prevent and respond to security incidents, appropriately scale computing resources and otherwise support and deliver this site and its services.

Cookies and Related Technologies

This site uses cookies and similar technologies to personalize content, measure traffic patterns, control security, track use and access of information on this site, and provide interest-based messages and advertising. Users can manage and block the use of cookies through their browser. Disabling or blocking certain cookies may limit the functionality of this site.

Do Not Track

This site currently does not respond to Do Not Track signals.


Pearson uses appropriate physical, administrative and technical security measures to protect personal information from unauthorized access, use and disclosure.


This site is not directed to children under the age of 13.


Pearson may send or direct marketing communications to users, provided that

  • Pearson will not use personal information collected or processed as a K-12 school service provider for the purpose of directed or targeted advertising.
  • Such marketing is consistent with applicable law and Pearson's legal obligations.
  • Pearson will not knowingly direct or send marketing communications to an individual who has expressed a preference not to receive marketing.
  • Where required by applicable law, express or implied consent to marketing exists and has not been withdrawn.

Pearson may provide personal information to a third party service provider on a restricted basis to provide marketing solely on behalf of Pearson or an affiliate or customer for whom Pearson is a service provider. Marketing preferences may be changed at any time.

Correcting/Updating Personal Information

If a user's personally identifiable information changes (such as your postal address or email address), we provide a way to correct or update that user's personal data provided to us. This can be done on the Account page. If a user no longer desires our service and desires to delete his or her account, please contact us at customer-service@informit.com and we will process the deletion of a user's account.


Users can always make an informed choice as to whether they should proceed with certain services offered by InformIT. If you choose to remove yourself from our mailing list(s) simply visit the following page and uncheck any communication you no longer want to receive: www.informit.com/u.aspx.

Sale of Personal Information

Pearson does not rent or sell personal information in exchange for any payment of money.

While Pearson does not sell personal information, as defined in Nevada law, Nevada residents may email a request for no sale of their personal information to NevadaDesignatedRequest@pearson.com.

Supplemental Privacy Statement for California Residents

California residents should read our Supplemental privacy statement for California residents in conjunction with this Privacy Notice. The Supplemental privacy statement for California residents explains Pearson's commitment to comply with California law and applies to personal information of California residents collected in connection with this site and the Services.

Sharing and Disclosure

Pearson may disclose personal information, as follows:

  • As required by law.
  • With the consent of the individual (or their parent, if the individual is a minor)
  • In response to a subpoena, court order or legal process, to the extent permitted or required by law
  • To protect the security and safety of individuals, data, assets and systems, consistent with applicable law
  • In connection the sale, joint venture or other transfer of some or all of its company or assets, subject to the provisions of this Privacy Notice
  • To investigate or address actual or suspected fraud or other illegal activities
  • To exercise its legal rights, including enforcement of the Terms of Use for this site or another contract
  • To affiliated Pearson companies and other companies and organizations who perform work for Pearson and are obligated to protect the privacy of personal information consistent with this Privacy Notice
  • To a school, organization, company or government agency, where Pearson collects or processes the personal information in a school setting or on behalf of such organization, company or government agency.


This web site contains links to other sites. Please be aware that we are not responsible for the privacy practices of such other sites. We encourage our users to be aware when they leave our site and to read the privacy statements of each and every web site that collects Personal Information. This privacy statement applies solely to information collected by this web site.

Requests and Contact

Please contact us about this Privacy Notice or if you have any requests or questions relating to the privacy of your personal information.

Changes to this Privacy Notice

We may revise this Privacy Notice through an updated posting. We will identify the effective date of the revision in the posting. Often, updates are made to provide greater clarity or to comply with changes in regulatory requirements. If the updates involve material changes to the collection, protection, use or disclosure of Personal Information, Pearson will provide notice of the change through a conspicuous notice on this site or other appropriate way. Continued use of the site after the effective date of a posted revision evidences acceptance. Please contact us if you have questions or concerns about the Privacy Notice or any objection to any revisions.

Last Update: November 17, 2020