Suppose a continuous random variable \(X\) is given by the PDF:

\[f(x) = \begin{cases} 2x \quad & x \in [0,1] \\ 0 \quad & \text{otherwise.} \end{cases}\]

If the mean of \(X\) is \(A\) and the variance of \(X\) is \(B\), what is \(A+B\)?

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