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Oct 1, 2015 at 10:10 comment added Douglas Zare How does it solve the problem to represent XY as a sum of uncorrelated random variables with known distributions?
Jun 16, 2011 at 20:20 comment added Tom LaGatta @Robert Israel, thank you for your comment. Of course, you are absolutely right. I have edited my response to fix this error.
Jun 16, 2011 at 20:20 history edited Tom LaGatta CC BY-SA 3.0
Corrected error as pointed out by Robert Israel
Jun 16, 2011 at 19:07 comment added Robert Israel No, the density of the sum of two independent random variables is the convolution of their density functions. Unfortunately, $X^2$ and $XZ$ are certainly not independent (although they are uncorrelated).
Jan 15, 2010 at 22:03 history answered Tom LaGatta CC BY-SA 2.5