Problems in Probability

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Fall 2011 Strategic Practice 8: Section 1 (Covariance and Correlation) - Question 1
Two fair six-sided dice are rolled (one green and one orange), with outcomes X and Y respectively for the green and the orange.
(a) Compute the covariance of X + Y and X - Y.
(b) Are X + Y and X - Y independent? Show that they are, or that they aren't (whichever is true).
Solution: (a) 0 (b) They are not independent: information about X + Y may give information about X - Y, by considering an extreme example.
"Mathematics is the logic of certainty, but statistics is the logic of uncertainty."
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