Finding correlation coefficient Two dice are thrown. $X$ denotes number on first die and $Y$ denotes maximum of the numbers on the two dice. Compute the correlation coefficient.

If $X \sim DiscreteUniform(1,6)$ and $Z \sim DiscreteUniform(1,6)$ are independent random variables, then their joint pmf, say $f(x,z)$ is: 
f = (1/6)*(1/6);   domain[f] = {{x, 1, 6}, {z, 1, 6}}  && {Discrete};

The desired correlation is then easy to compute using automated tools:
Corr[{x, Max[x, z]}, f]

returns:  $3 \sqrt{\frac{3}{73}}$ which is approximately 0.608 ...
Notes


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*The Corr function used above is from the mathStatica package for Mathematica. As disclosure, I should add that I am one of the authors.

