其實有趣的地方是:
若 E[X] = 1 - E[X] => E[X] = 1/2
若 F (x) = x, 0 < x < 1 = > f (x) = 1, 0 < x < 1
X x
1 1
=> E[X] = S x f(x) dx = S x dx = 1/2
0 0
F (y) = y, 0 < y < 1 => E[Y] = 1/2 (同樣的流程)
Y
Y = 1 - X => E[Y] = E[1-X] = E[1] - E[X] = 1 -E[X]
而 1/2 = 1- 1/2 ?
對不對?
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