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If the expectation of the norm of random variable is bounded, does that imply that the expectation of the squared norm is bounded?
Let $\mathbf{x}$ be a random vector. If $\mathbb{E}[\|\mathbf{x}\|]$ is upper bounded, does that imply that $\mathbb{E}[\|\mathbf{x}\|^2]$ is also upper bounded?
The Jensen's inequality goes the ...