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Results tagged with inequalities
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user 12264
for questions involving inequalities, upper and lower bounds.
0
votes
1
answer
230
views
a simple probability inequality
For independent Rademacher random variables $\epsilon_i, i=1,2, \cdots, n$, i.e. $P(\epsilon_i=-1)=P(\epsilon_i=1)=\frac{1}{2}$, do we have
$$max_{0\le a_i\le b, i=1,2,\cdots,n}P(|\sum_{i=1}^n\epsil …
- 105
6
votes
2
answers
552
views
Inequality involving the weak second moment
I want to ask the following probability inequality:
Is it true that for any random variable $X\ge 0$, we have
$$
\sup_{t>0}(t\mathbb E(X\mathbf 1_{X\ge t}))
\le
2\sup_{t>0}(t^2 \mathbb P(X \ge t …
- 105