My Math Forum Simple equivalence to verify.

 November 22nd, 2014, 08:29 AM #1 Newbie   Joined: Nov 2014 From: Rome, Italy Posts: 1 Thanks: 0 Simple equivalence to verify. Hi everyone, I am new in here and I hope some of you may help me with this. Let A,B and C be three events such that the following three inequalities are verified: P(A|BC)>P(A|\BC) P(A|B\C)>P(A|\B\C) P(A|B)t+s) B=(X=x) C=(Y=y) and D=(x<=X<=x')$\displaystyle \cap$(y<=Y<=y')$\displaystyle \cap$(T>t) and if we apply the previous inequalities to the conditional probability $\displaystyle P(\cdot|D)$, they become equivalent to say that $\displaystyle P(T>t+s|T>t,X=x,Y=y)$ is strictly decreasing in x for every y and $\displaystyle P(T>t+s|T>t,X=x)$ is increasing in x. I don't understand what it means to apply those inequalities to the conditional probability $\displaystyle P(\cdot|D)$ and, even if I did, I am not sure I'd be able to verify such equivalence. Hope some of you want to help! Thank you in advance
 November 29th, 2014, 12:03 AM #2 Senior Member   Joined: Aug 2012 Posts: 229 Thanks: 3 Hey Vivi. Can you please re-summarize what you are trying to do and what you are trying to understand?

 Tags equivalence, inequality, probability, simple, verify

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