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The random variable \(X\) has the density \( f(x) = \frac{x}{2} \), on the interval \([0, 2]\). Calculate \(E(X)\).\FieldText{1}{$$\begin{aligned}[t] E(X) &= \int_{0}^{2} x \frac{x}{2} \, dx \\ &= \frac{1}{2} \int_{0}^{2} x^2 \, dx \\ &= \frac{1}{2} \left[ \frac{x^3}{3} \right]_{0}^{2} \\ &= \frac{1}{2} \left( \frac{2^3}{3} - \frac{0^3}{3} \right) \\ &= \frac{1}{2} \cdot \frac{8}{3} \\ &= \frac{4}{3} \end{aligned}$$}