ee230_slides_chapter3.pdf - Continuous Random Variables and PDFs Cumulative Distribution Functions Normal Random Variables Multiple Continuous Random

ee230_slides_chapter3.pdf - Continuous Random Variables and...

This preview shows page 1 - 7 out of 107 pages.

Continuous Random Variables and PDFs Cumulative Distribution Functions Normal Random Variables Multiple Continuous Random Variables Conditioning The Continuous Bayes’ Rule . . EE 230 General Random Variables Department of Electrical and Electronics Engineering Middle East Technical University April 21, 2016 1/75
Image of page 1
Continuous Random Variables and PDFs Cumulative Distribution Functions Normal Random Variables Multiple Continuous Random Variables Conditioning The Continuous Bayes’ Rule . General Random Variables Random variables with a continuous range of possible values are quite common, e.g., thermal noise current intrinsic to all resistors (due to heating of a resistor), your exact weight, .... In fact, some discrete random variables are obtained through some operation on continuous ranges. The use of continuous models may result in insights that would not be possible with discrete modeling. All of the concepts and tools introduced for discrete random variables have continuous counterparts. 2/75
Image of page 2
Continuous Random Variables and PDFs Cumulative Distribution Functions Normal Random Variables Multiple Continuous Random Variables Conditioning The Continuous Bayes’ Rule Properties of PDF Some Continuous Random Variables and Their PDFs Expectation . Continuous Random Variables and PDFs . Example . . Angle of an arbitrarily drawn line. Consider that all outcomes are equally likely. What is the probability that the angle will be less than π ? 3/75
Image of page 3
Continuous Random Variables and PDFs Cumulative Distribution Functions Normal Random Variables Multiple Continuous Random Variables Conditioning The Continuous Bayes’ Rule Properties of PDF Some Continuous Random Variables and Their PDFs Expectation . Continuous Random Variables and PDFs . Definition . . A random variable X is continuous if there is a nonnegative func. f X , called the probability density function (PDF) of X , such that P ( X B ) = B f X ( x ) dx , for every subset B of the real line. In particular, P ( a X b ) = b a f X ( x ) dx 4/75
Image of page 4
Continuous Random Variables and PDFs Cumulative Distribution Functions Normal Random Variables Multiple Continuous Random Variables Conditioning The Continuous Bayes’ Rule Properties of PDF Some Continuous Random Variables and Their PDFs Expectation . Continuous Random Variables and PDFs . Definition . . A random variable X is continuous if there is a nonnegative func. f X , called the probability density function (PDF) of X , such that P ( X B ) = B f X ( x ) dx , for every subset B of the real line. In particular, P ( a X b ) = b a f X ( x ) dx (area under the PDF) 4/75
Image of page 5
Continuous Random Variables and PDFs Cumulative Distribution Functions Normal Random Variables Multiple Continuous Random Variables Conditioning The Continuous Bayes’ Rule Properties of PDF Some Continuous Random Variables and Their PDFs Expectation .
Image of page 6
Image of page 7

You've reached the end of your free preview.

Want to read all 107 pages?

  • Fall '19

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern

Stuck? We have tutors online 24/7 who can help you get unstuck.
A+ icon
Ask Expert Tutors You can ask You can ask You can ask (will expire )
Answers in as fast as 15 minutes