baiyang11
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Consider N random variables X_{n} each following a Bernoulli distribution B(r_{n}) with 1 \geq r_{1} \geq r_{2} \geq ... \geq r_{N} \geq 0. If we make following assumptions of sets A and B:
(1) A \subset I and B \subset I with I=\{1,2,3,...,N\}
(2) |A \cap I_{1}| \geq |B \cap I_{1}| with I_{1}=\{1,2,3,...,n\}, n<N
(3) |A|=|B|=n
Do we have \mathbb{E}(\Sigma_{a\in A} X_{a}) \geq\mathbb{E}(\Sigma_{b\in B} X_{b})?
To avoid confusion, \mathbb{E} means expected value.Thanks!
(1) A \subset I and B \subset I with I=\{1,2,3,...,N\}
(2) |A \cap I_{1}| \geq |B \cap I_{1}| with I_{1}=\{1,2,3,...,n\}, n<N
(3) |A|=|B|=n
Do we have \mathbb{E}(\Sigma_{a\in A} X_{a}) \geq\mathbb{E}(\Sigma_{b\in B} X_{b})?
To avoid confusion, \mathbb{E} means expected value.Thanks!