A four-sided (tetrahedral) die has a different number 1, 2, 3, or 4 affixed to each side. On any given roll, each of the four numbers is equally likely to occur. Let e = (i, j) represent an arbitrary outcome resulting from two rolls of the four-sided die. Tabulate the discrete probability density function and sketch the graph of the cumulative distribution function for the random variable W(e)=(i - j)2 .
Added by Julio B.
Step 1
(i, j) can be any pair from {(1,1), (1,2), (1,3), (1,4), (2,1), (2,2), (2,3), (2,4), (3,1), (3,2), (3,3), (3,4), (4,1), (4,2), (4,3), (4,4)}. The corresponding W(e) values are {0, 1, 4, 9, 1, 0, 1, 4, 4, 1, 0, 1, 9, 4, 1, 0} respectively. Show more…
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