X is a uniform variate between 0 and 3. The value of E(X²) is?
- 3
- 7
- 27
- 9
Explanation
Since X is a uniform variate between 0 and 3, the probability density function (pdf) of X is:
f(x) = 1/3 for 0 ≤ x ≤ 3
To find E(X²), we need to calculate the expected value of X², which is:
E(X²) = ∫x²f(x)dx = ∫(x²/3)dx from 0 to 3
Evaluating the integral, we get:
E(X²) = (1/3)∫x²dx from 0 to 3 = (1/3)[(3³)/3] = 3
So, the expected value of X² is 3.
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