lecture 22 - properties of expectation IV.pdf

lecture 22 - properties of expectation IV.pdf - Stor 435...

This preview shows page 1 - 4 out of 10 pages.

Stor 435: Introduction to Probability Lecture 22: Properties of expectation - IV Vladas Pipiras UNC-CH November 27, 2018 Vladas Pipiras (UNC) Stor 435: Lecture 22 1 / 10
Image of page 1

Subscribe to view the full document.

Properties of expectation Prediction problem: Y is unobservable random variable, X is observable random variable (related to Y ). Provide the best guess (predictor) of Y based on X , that is, g ( X ) such that E ( Y - g ( X )) 2 is smallest. E ( Y | X ) and prediction E ( Y - g ( X )) 2 E ( Y - E ( Y | X )) 2 , that is, E ( Y | X ) is the best predictor of Y given X . Vladas Pipiras (UNC) Stor 435: Lecture 22 2 / 10
Image of page 2
Properties of expectation Example 6b: Suppose that if a signal value s is sent from location A , then the signal value received at location B is normally distributed with parameters ( s , 1). If S , the value of the signal sent at A , is normally distributed with parameters ( μ, σ 2 ), what is the best estimate of the signal sent if R , the value received at B , is equal to r ? Vladas Pipiras (UNC) Stor 435: Lecture 22 3 / 10
Image of page 3

Subscribe to view the full document.

Properties of expectation Moment generating function A moment generating function (m.g.f.) of a random variable
Image of page 4
You've reached the end of this preview.

{[ snackBarMessage ]}

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