Normal Distribution PDF and its Moment Generating Function

May 5th, 2015
Studypool Tutor
Texas A & M University
Price: $10 USD

Tutor description

A walk through of normal distribution, and its PDF is provided. The moment generating function of normal distribution is derived. This is a work in progress, and depending upon response I will add more examples. So far it consists of 10 pages and 8 examples. Feedback is welcome.

Word Count: 1794
Showing Page: 1/10
Normal Distribution PDF and its Moment GeneratingFunctionDraft copybyStudent HelperApril 2015c2015Student Helper. All rights reserved.Chapter 1PDF and Moment GeneratingFunctionOne of the most common continous distributions that you will incur in engineering, science and statistics is the normal distribution. The normal distributionis sometimes informally called as the bell curve owing to its bell-shaped look.In this chapter, a brief introduction to the different properties of a normal distribution is provided. In the subsequent chapters, we will look at some of theseproperties in details.1.1Normal PDF and its characteristicsA continuous distribution is usually defined in terms of its probability densityfunction or PDF. Let X be normally distributed random variable, with mean and standard deviation . Then, the PDF, fX (x) of the normally distributedrandom variable X is of the form:1fX (x) = 21 x !2e 2.(1.1)Possibly, the simplest of all normally distributed random variables are theones known as the standard normal variables. For these variables, = 0, and = 1, and the equation 1.1 simplifies to:x21fX (x) = e 2 .21(1.2)0.45 = 0, = 1 = 0, = 2 = 0, = 3 = 1, = 1 = 2, = 2 = 3, = 30.40.350.3PDF0.250.20.150.10.0501086420246810XFigure 1.1: The PDF of normal distributions corresponding to six sets

Review from student

Studypool Student
" Thanks for the help. "
Ask your homework questions. Receive quality answers!

Type your question here (or upload an image)

1820 tutors are online

Brown University





1271 Tutors

California Institute of Technology




2131 Tutors

Carnegie Mellon University




982 Tutors

Columbia University





1256 Tutors

Dartmouth University





2113 Tutors

Emory University





2279 Tutors

Harvard University





599 Tutors

Massachusetts Institute of Technology



2319 Tutors

New York University





1645 Tutors

Notre Dam University





1911 Tutors

Oklahoma University





2122 Tutors

Pennsylvania State University





932 Tutors

Princeton University





1211 Tutors

Stanford University





983 Tutors

University of California





1282 Tutors

Oxford University





123 Tutors

Yale University





2325 Tutors