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Results tagged with inequalities
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user 39261
for questions involving inequalities, upper and lower bounds.
6
votes
Accepted
Lower bound for the $p$-th absolute moment of a sum of random variables
If the $X_i$ are i.i.d. Gaussian with variance $1$, then you have
$$ c_p := \mathbb{E} |X_k|^p = \frac{2^{p/2} \Gamma(\frac{p+1}{2})}{\sqrt{\pi}}.$$
The variable $S_n$ is also Gaussian with variance $ …
- 2,306
10
votes
3
answers
791
views
Discrete entropy of the integer part of a random variable
Let $X$ be a real valued random variable. Of course, the integer part $\lfloor X \rfloor$ of $X$ is a discrete random variable taking values in $\mathbb{Z}$. We can therefore define its discrete entro …
- 2,306