My Math Forum Expected Value, Difficulty with Notation in Text

 February 21st, 2016, 07:39 PM #1 Senior Member   Joined: Jan 2014 Posts: 196 Thanks: 3 Expected Value, Difficulty with Notation in Text In Shelton M Ross, Introduction to Prob Models 11th edition, I am in 2.5.3, reading about Covariance. Would $\displaystyle E[XY] = \sum xyp(x,y)$? Thank you for any help.
 February 21st, 2016, 10:56 PM #2 Senior Member   Joined: Dec 2012 From: Hong Kong Posts: 853 Thanks: 311 Math Focus: Stochastic processes, statistical inference, data mining, computational linguistics Yes, I think so, by the definition of expected value (though that's not the covariance).
 February 22nd, 2016, 10:36 AM #3 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 Given any function, f, of the random variables, x, y, with probability given by p(x,y), the "expected value of f" is $\sum f(x,y)p(x,y)$ where the sum is over all values of x and y. (This is assuming discrete variables, taking either finite or countable variables. If the variables are continuous, $\int\int xyp(x,y)dxdy$.)

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