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Results tagged with inequalities
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user 129831
for questions involving inequalities, upper and lower bounds.
14
votes
3
answers
2k
views
How to prove $e^x\left|\int_x^{x+1}\sin(e^t) \,\mathrm d t\right|\le 1.4$?
Related question asked by me on Math SE a few days ago: How to prove $e^x\left|\int_x^{x+1}\sin(e^t) \,\mathrm d t\right|\le 1.4$?
A few days ago, somebody asked How to prove $ \mathrm{e}^x\left|\int …
- 1,326
2
votes
1
answer
233
views
Kolmogoroff condition for truncated random variables
Question summary. Does the Kolmogoroff condition $\sum_{n=1}^\infty\frac{\mathbb V Y_n}{n^2} < \infty$ hold for truncated random variables $Y_n := X_n \cdot 1_{\{X_n \le n\}}$ (see below for a more ri …
- 1,326
2
votes
1
answer
220
views
Does the inequality $\mu F(\mu)^2\geq \int_{\mu}^{b}F(x)\cdot(1-F(x))\,\mathrm dx$ hold for ...
This question was originally asked on the Mathematics StackExchange by User smcc
Consider a continuous random variable $V$ with cumulative distribution function $F$ and density function $f$. Suppose …
- 1,326
1
vote
A four-variable maximization problem
By Cauchy-Schwarz for sums (with $x_i=\sqrt{a+b}$ and $y_i=\sqrt{a+c}\sqrt{a+d}$, also, I am using cyclic sum notation):
\begin{split}
f(a,b,c,d)&=\sum_{\text{cyc}} \sqrt{(a+b)(a+c)(a+d)}\\&\le \left( …
- 1,326