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rangatudugala
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How to prove this "if p(a)=p(b)=p then p(ab) ≤ p^2
Right.rangatudugala said:so you trying to explain that p(null set) = 0 so its not good example is it ?
okay i think i got the answerRUber said:Right.
If p(a) = p(b) and the problem doesn't state that a is not b, then a = b should be your first example.
Look at post 7. Assume 0<p<1 to eliminate the option for p = p^2.
rangatudugala said:How to prove this "if p(a)=p(b)=p then p(ab) ≤ p^2Homework Equations
The Attempt at a Solution
rangatudugala said:okay i think i got the answer
so
1/ if a, b mutually exclusive then p(a∩b) =0
2/ if a,b independent then p(a∩b)= p(a)*p(b) =p^2
is it ?
okay I'm fail to prove that can you please tell me how to do that ?Ray Vickson said:Please use different letters: use ##P(a)## and ##P(b)## for the probabilities of ##a## and ##b##, but the letter ##p## for their value; that is, you should say ##P(a) = P(b) = p##. That will avoid a lot of confusion.
Both of your examples obey ##P(a \cap b) \leq p^2##. But: are you finished? No: you have not proved that ##P(a \cap b) \leq p^2 ## for all possible cases where ##P(a) = P(b) = p##, nor have you discovered a counterexample (that is, an example where ##P(a \cap b) > p^2##).
rangatudugala said:okay I'm fail to prove that can you please tell me how to do that ?
Ray Vickson said:No. We are not permitted to solve problems for students---we are allowed to give hints, but nothing more. (Anyway, to be honest, I cannot see how to deal with the problem right now!)
Are you sure about this?rangatudugala said:independent
also P(a/b) = P(a)* P(a ∩ b) / P(b) ---> 3
P(b/a) = P(b)* P(a ∩ b) / P(a) ---> 4
P(a/b) means probability of a given b, right? yes its trueRUber said:Are you sure about this?
Your notation P(a/b) means probability of a given b, right?
This implies that P(a/b) = P(a ∩ b). Shouldn't it just be P(a/b) = P(a ∩ b) / P(b)?