Question about probability of union

AI Thread Summary
The discussion centers on the probability of the union of two events involving positive random variables x1 and x2. The question posed is whether P(A U B) can be equated to P(x1 + x2 > k). Participants clarify that P(A U B) represents the probability that either event A or event B occurs, but adding inequalities does not yield the desired result. The consensus is that the proposed equation does not hold true, and the reasoning behind this is that inequalities cannot be simply combined in this manner. The conversation concludes with an acknowledgment of the misunderstanding regarding the addition of inequalities.
St41n
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If x1, x2 positive random variables and we have the following two events:

A={x1 > δ}
B={x2> k-δ}

where 0<δ<k

then is it true that:

P(A U B) = P( x1+x2 > δ+(k-δ)=k ) ?

If true can you explain why is that?
Thank you
 
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Hi St41n! :wink:

No, P(A U B) means the probability that either A or B is true.

So P(A U B) = P(x1 > 1 or x2 > 1). :smile:
 
yes i know this is the definition of P(A U B), but does it imply anything about the sums when we have inequalities?

Also, I made some changes to my original post. Can you take a look again?
 
St41n said:
… when we have inequalities?

You can't add inequalities like that, it just doesn't work.
Also, I made some changes to my original post. Can you take a look again?

Sorry, still doesn't work.
 
Ok I see, thanks
 

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