Lecture_10-1 - 1 ISE 690 Statistical Methods for Engineers...

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1 Industrial and Systems and Engineering Management Department Fall 15 Dilcu Helvaci Barnes (Email: [email protected]) ISE 690 Statistical Methods for Engineers Covariance and Correlation
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2 Covariance When two or more random variables are defined on a probability space, it is useful to describe how they vary together; that is it is useful to measure the relationship between the variables. A common measure of the relationship between two random variables is the covariance.
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3 Covariance The covariance is defined for both continuous and discrete random variables by the same formula. The covariance between the random variables X and Y, denoted as Cov(X,Y) or
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4 Example For the joint probability distribution of the two random variables in following, calculate Cov(X,Y). x= Number of Bars of Signal Strength y= Response Time(neare st second) 1 2 3 4 0.15 0.10 0.05 3 0.02 0.10 0.05 2 0.02 0.03 0.20 1 0.01 0.02 0.25
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5 Solution
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6 Solution
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7 Covariance (Linear Relationship) Covariance is a measure of linear relationship between the random variables.
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  • Fall '15
  • DilcuBarnes
  • Probability theory, Wiley & Sons, Systems and Engineering Management, Helvaci Barnes

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