If one fair six-sided die is rolled, suppose that X is the total number of even

Question

If one fair six-sided die is rolled, suppose that X is the total number of even numbers shown and Y is the total number of fives shown. Explain intuitively why the correlation of X and Y should be negative, then calculate the correlation exactly in terms of p1 and p2.

Hint: For the second part, notice that E(XY ) = 0. Explain why this is true and use this fact in your calculation.

I don't understand because if one die is rolled, then the total number of evens shown is either 1 or 0, the same can be said for the number of fives shown. So, how can expected values be obtained from this, as the probabilities would both be 1/6?

Explanation / Answer

If one fair six-sided die is rolled, suppose that X is the total number of even numbers shown and Y is the total number of fives shown. Explain intuitively why the correlation of X and Y should be negative, then calculate the correlation exactly in terms of p1 and p2. X is the total number of even numbers In our die total number of even numbers are 3 those are 2,4 and 6. So X takes 2,4,6 Y is the total number of fives shown In a die total number of fives shown is 1

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