# calculating correlation

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.

How can I go about calculating the correlation exactly in terms of $p_1$ and $p_2$?

I was given, Hint: Notice that $E(XY) = 0$. Explain why this is true and use this fact in your calculation.

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• The covariance is $E[(X-E[X])(Y-E[Y])] = E[XY]-E[X]E[Y]$
• For a Bernoulli random variable which is $1$ with probability $p$ and $0$ with probability $1-p$, the expectation is $p$ and the standard deviation is $\sqrt{p(1-p)}$
@ulc8: The covariance is $0-\frac12 \times \frac16 = -\frac{1}{12}$ so the correlation coefficient will also be negative. And it the standard deviations not the variances which are $\frac12$ and $\sqrt{\frac{5}{36}}$ –  Henry Dec 3 '12 at 22:30