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It is used in the following way, given subsets of the sample space $$A_1, \cdots, A_n \subset \Omega$$ such that $\mathbb{P}(A_i) \leq \theta$.

Now define i.i.d. Bernoulli r.v.s $B_i \sim Ber(\theta)$, then $$(\chi_{A_1} , \cdots, \chi_{A_n}) \leq_{ST} (B_1, \cdots, B_n).$$

What does this $\leq_{ST}$ mean precisely?

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  • $\begingroup$ Probably "stochastic domination." I don't remember the definition though. $\endgroup$ – Will M. Apr 10 at 18:53
  • $\begingroup$ It's called stochastic order, just look it up. $\endgroup$ – dnqxt Apr 10 at 18:58
  • $\begingroup$ Thank you all . $\endgroup$ – Xiao Apr 10 at 19:28

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