Hi people. Can you help me realize why this is true? I can tell you that $P\_i$ and $P\_j$ are probabilities, i.e. $0 \leq P\_i, P\_j \leq 1$.

$\displaystyle \sum\_{i=1}^\infty \sum\_{j=1}^\infty ijP\_iP\_j \leq \sum\_{i=1}^\infty \sum\_{j=1}^\infty j^2P\_jP\_i$.