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November 22nd, 2014, 08:29 AM   #1
Joined: Nov 2014
From: Rome, Italy

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Lightbulb 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:
where "\B"= complementary of B, "\C"= complementary of C.
Now, if we define
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
$\displaystyle P(T>t+s|T>t,X=x)$ 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
Vivi is offline  
November 29th, 2014, 12:03 AM   #2
Senior Member
Joined: Aug 2012

Posts: 229
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Hey Vivi.

Can you please re-summarize what you are trying to do and what you are trying to understand?
chiro is offline  

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