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Probability Distributions



June 19, 2015 to July 17, 2015 January 29, 2016 to February 26, 2016 June 17, 2016 to July 15, 2016 January 27, 2017 to February 24, 2017 January 26, 2018 to February 23, 2018 June 22, 2018 to July 20, 2018

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Probability Distributions

taught by Madhav Kulkarni

Aim of Course:

This online course, "Probability Distributions" will cover statistical probability distributions, such as the Bernoulli distribution, uniform distribution, hypergeometric distribution, Poisson distribution, Normal distribution, exponential distribution, Gamma distribution, Weibull distribution, Student's t distribution, chi-square distribution, F-distribution. Participants will learn how to identify which distribution(s) reasonably fit given data, and to evaluate the fit.

Course Program:

WEEK 1: Introduction to Random Experiments and Random Variables (Discrete and Continuous)

  • Probability distribution
  • Properties and applicability
  • Bernouli and discrete uniform distribution

WEEK 2: Binomial, Poisson and Hypergeometric Distributions

  • Binominal
  • Hypergeometric
  • Poisson and geometric random variables
  • Identification and application of these distributions

WEEK 3: Normal, Exponential, Gamma and Weibull Distributions

  • Normal
  • Exponential
  • Gamma
  • Weibull
  • Identification and application of these distributions

WEEK 4: Derived Distributions

  • Introduction and applicability
  • Student's distribution
  • Chi-square distribution and F-distribution
  • Importance and applications
  • Identification and appropriate distribution


Homework in this course consists of short answer questions to test concepts, guided data analysis problems using software, and end of course project.

In addition to assigned readings, this course also has practice exercises, an end of course data modeling project, example software codes, and supplemental readings available online.

Probability Distributions


June 19, 2015 to July 17, 2015 January 29, 2016 to February 26, 2016 June 17, 2016 to July 15, 2016 January 27, 2017 to February 24, 2017 January 26, 2018 to February 23, 2018 June 22, 2018 to July 20, 2018

Course Fee: $629

Do you meet course prerequisites? What about book & software? (Click here to learn more)

Tuition Savings:  When you register online for 3 or more courses, $200 is automatically deducted from the total tuition. (This offer cannot be combined and is only applicable to courses of 3 weeks or longer.)

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Courses may fill up at any time and registrations are processed in the order in which they are received. Your registration will be confirmed for the first available course date, unless you specify otherwise.

Probability Distributions

taught by Madhav Kulkarni

Who Should Take This Course:

Anyone who models data or statistical processes.



These are listed for your benefit so you can determine for yourself, whether you have the needed background, whether from taking the listed courses, or by other experience.

If you are unclear as to whether you have mastered the above requirements, try these placement tests.

Some familiarity with calculus (see statistics.com's brief Calculus Review course) is helpful for a complete facility with the various distributions.

Organization of the Course:

This course takes place online at the Institute for 4 weeks. During each course week, you participate at times of your own choosing - there are no set times when you must be online. Course participants will be given access to a private discussion board. In class discussions led by the instructor, you can post questions, seek clarification, and interact with your fellow students and the instructor.

At the beginning of each week, you receive the relevant material, in addition to answers to exercises from the previous session. During the week, you are expected to go over the course materials, work through exercises, and submit answers. Discussion among participants is encouraged. The instructor will provide answers and comments, and at the end of the week, you will receive individual feedback on your homework answers.

Time Requirement: about 15 hours per week, at times of  your choosing.

Students come to the Institute for a variety of reasons. As you begin the course, you will be asked to specify your category:
  1. You may be interested only in learning the material presented, and not be concerned with grades or a record of completion.
  2. You may be enrolled in PASS (Programs in Analytics and Statistical Studies) that requires demonstration of proficiency in the subject, in which case your work will be assessed for a grade.
  3. You may require a "Record of Course Completion," along with professional development credit in the form of Continuing Education Units (CEU's).  For those successfully completing the course, 5.0 CEU's and a record of course completion will be issued by The Institute, upon request.

Course Text:
Required text for this course is Introduction to Discrete Probability and Probability Distributions, First Edition by Madhav B. Kulkarni and Surendra B. Ghatpande, published 2007 by SIPE Academy, Publishers and Consultants, Nashik.  The text will be made available as a .pdf during the first lesson.


Any general statistical package can perform most of the operations called for in this course, which fall into two main categories: (1) generation, tabling and graphing of random variables from specified distributions, (2) calculating probabilities, assessing fit, and performing statistical tests. Also note that Excel can be used for much of the above, particularly when coupled with Resampling Stats for Excel. Finally, R functions are provided as part of the course; these can be used for most of the course work if you have some basic familiarity with R. Click here for download information for these and other software packages that offer free or nominal cost versions that may be used in statistics.com courses.

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