Question about probability of union

[St41n]

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

 

[tiny-tim]

Hi St41n!

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).

 

[St41n]

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?

 

[tiny-tim]

… 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.

 

[St41n]

Ok I see, thanks