设X的概率密度函数为f(x)={x,0

期望 E(X) = ∫xf(x) dx = ∫x?dx + ∫(2x-x?) dx = 1/3 + 2/3 =1再计算E(X?) = ∫x?f(x) dx = ∫x?dx + ∫(2x?-x?) dx = 1/4 + (14/3 - 15/4) = 7/6所以方差 D(X) = E(X?)-E(X)?= 7/6 -1?= 1/6

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