Is it intuitive that given the occurence of an event A, the probability that p(A) is less than x is equal to min(x,1) for non-negative x?
Intuition sucks.
Update: The post initially appeared in a weird manner coz Blogger refused to recognize 'lesser than' and 'greater than' symbols and instead read it as a html tag. Found the error on reading yhac's second comment.
Intuition sucks.
Update: The post initially appeared in a weird manner coz Blogger refused to recognize 'lesser than' and 'greater than' symbols and instead read it as a html tag. Found the error on reading yhac's second comment.
posted by eV at 9:13 AM
7 Value-adds:
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Did you mean p(A) or p(A|A)? How is either 0?
1. Occurence of event A is given - Hence, no intuition required.
2. Due to point 1, p(A) is also known - No intuition required once again.
3. x is not given. But by intuition, we more less "presume" intuitively that x is a positive integer.
4. By virtue of the intuition referred to in point 3, we usually get a clear YES or NO answer to the question posted.
Intuition alone did the trick here. Good or bad, is a different story.
Dhi, Not quite. "Given that an event A occurs" !=> p(A)=1.
For example, if A = Heads on toss of a coin, "Given that A occurs" only means that the coin was tossed and it resulted in Heads.
The statement just says the density of the continuous random variable "Probability of occurence of an event A" is uniform.. Seems pretty intuitive to me. Given an event the pdf of the probability of the event should be uniform on [0,1] as any possible pdf could be assigned to the random variable A.
eV>> p(A) = 1 yes. And that is what my point 2 says. That p(A) is known. My point does not bother with the value. Continue further and the reasoning holds!
madatadam, I am not saying it isn't intuitive da. Just that intuition sucks. And btw, when you say pdf, all I can think of is Adobe. :)
Dhi, Apo ok.
Chilli, Please translate - if required. :p
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