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.