{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Review2_Study_Guide

Review2_Study_Guide - ORIE 3500/5500 Fall Term 2008 Review...

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
ORIE 3500/5500 Fall Term 2008 Review 2 Multivariate Normal A vector ( X 1 , . . . , X k ) is said to follow a multivariate normal distribution if any linear combination of the components, e.g. Y = a 1 X 1 + · · · + a k X k for some constants a 1 , . . . , a k , has normal distribution. The parameters of the multivariate normal distribution are (a) the mean vector μ and (b) covariance matrix Σ μ = μ 1 μ 2 . . . μ k , Σ = σ 11 σ 12 · · · σ 1 k σ 21 σ 22 · · · σ 2 k . . . . . . . . . σ k 1 σ k 2 · · · σ kk , and the notation is X = X 1 X 2 . . . X k N k [ μ, Σ ] . The interpretation of the parameters are μ i = E ( X i ) , σ ij = cpv ( X i , X j ) , 1 i, j k. Three important things to remember: 1. Suppose Y = ( Y 1 , . . . , Y r ) T be such that each com ponent of Y is some linear cpmbination of the components of X , e.g. Y = Y 1 Y 2 . . . Y r = a 11 X 1 + · · · + a 1 k X k a 21 X 1 + · · · + a 2 k X k .
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ 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