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X is a uniformly distributed random variable that takes values between 0 and 1. The value of E[X³] will be

1. 0
2. 1/8
3. 1/4
4. 1/2

Correct answer: 1/4

Solution

For X uniform on (0,1), E[X^3] = integral_0^1 x^3 dx = 1/4. The stored value 1/8 is E[X^3] computed incorrectly; the correct answer is 1/4.

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