Transcript Lecture 12
ASEN 5070: Statistical Orbit Determination I Fall 2015 Professor Brandon A. Jones Lecture 12: Probability and Statistics (Part 2) University of Colorado Boulder Lecture Quiz Due 5pm on Friday Homework 4 Due Friday University of Colorado Boulder 2 PDF Moments University of Colorado Boulder 3 Probability of X in [x,x+dx]: where f(x) is the probability density function (PDF) For CRVs, the probability axioms imply: University of Colorado Boulder 4 The expected value is a weighted average of all possible values to determine the mean Define the k-th moment about the origin as University of Colorado Boulder 5 We define the k-th moment about the mean: The second moment about the mean is also known as the variance: University of Colorado Boulder 6 University of Colorado Boulder 7 Although not traditionally examined, higher-order moments are becoming increasingly important in orbit determination… University of Colorado Boulder 8 University of Colorado Boulder 9 If a and b are constants (or equivalently independent of X ), then University of Colorado Boulder 10 University of Colorado Boulder 11 University of Colorado Boulder 12 Example Distributions University of Colorado Boulder 13 Images: Wikicommons University of Colorado Boulder 14 PDF CDF Images: Wikicommons University of Colorado Boulder 15 Images: Wikicommons University of Colorado Boulder 16 University of Colorado Boulder 17 Example Problems University of Colorado Boulder 18 University of Colorado Boulder 19 University of Colorado Boulder 20 University of Colorado Boulder 21 University of Colorado Boulder 22 University of Colorado Boulder 23 University of Colorado Boulder 24 University of Colorado Boulder 25 University of Colorado Boulder 26 University of Colorado Boulder 27 University of Colorado Boulder 28