let X be difference between two die rolls
a)
outcome | X | P(X) |
(1,6) | -5 | 1/36 |
(1,5)(2,6) | -4 | 2/36 |
(1,4)(2,5)(3,6) | -3 | 3/36 |
(1,3)(2,4)(3,5)(4,6) | -2 | 4/36 |
(1,2)(2,3)(3,4)(4,5)(5,6) | -1 | 5/36 |
(1,1)(2,2)(3,3)(4,4)(5,5)(6,6) | 0 | 6/36 |
(2,1)(3,2)(4,3)(5,4)(6,5) | 1 | 5/36 |
(3,1)(4,2)(5,3)(6,4) | 2 | 4/36 |
(4,1)(5,2)(6,3) | 3 | 3/36 |
(5,1)(6,2) | 4 | 2/36 |
(6,1) | 5 | 1/36 |
b)
expected value = Σx*P(X) = -5*1/36 + (-4)*2/36+.........................+5*1/36 =0.00
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