All Questions
2
questions
1
vote
1
answer
609
views
Find an upper bound on the expectation of squared norm given an upper bound on the expectation of norm
For non-independent random vectors $X, Y$, I have an upper bound on the expectations $E[\|X\|_2] \leq a, E[\|Y\|^2_2] \leq b$. How can I compute an upper bound for $E[\|X^\intercal Y\|_2]$ or $E[\|X^\...
2
votes
2
answers
673
views
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 ...