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Apr
16
comment Probability Theory: How to prove inequality $\mathbb{E}|X - m|^3 \leq \mathbb{E}|X|^3 (1 + \frac{m}{\sigma})^3$
I thought to use function $(E|X|^u)^{\frac{1}{u}}$ to prove this inequality, but I stuck at $\sigma$ existence in right part
Apr
16
comment Probability Theory: How to prove inequality $\mathbb{E}|X - m|^3 \leq \mathbb{E}|X|^3 (1 + \frac{m}{\sigma})^3$
@Did I think about using function $(\mathbb{E}|X|^u)^\frac{1}{u}$ for this. But after a while I can't prove $\sigma$ existence in right part.
Mar
13
comment Probability Theory: Cramer Transform Issue and deviation probabilities theory.
Is it needed to approximate...