SOLUTION: a six sided die is rolled twice. let Y and Z be the value of the first and second rolls, and let X be the maximum of the two. Please help me find the Variance of X.

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Question 429457: a six sided die is rolled twice. let Y and Z be the value of the first and second rolls, and let X be the maximum of the two.
Please help me find the Variance of X.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Consider the ordered pair (y,z). By constructing a table of ordered pairs (y,z), where y = 1,2,3,4,5,6, and z = 1,2,3,4,5,6, it is found that the pmf is
x ------> 1 2 3 4 5 6
p(x)----> 1/36 3/36 5/36 7/36 9/36 11/36
==> mu+=+E%28X%29+=+1%2F36+%2B+6%2F36+%2B+15%2F36+%2B28%2F36+%2B+45%2F36+%2B+66%2F36+=+161%2F36
==> , to 5 decimal places.