Sunday, February 05, 2006

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.

7 Value-adds:

Blogger yhac said...

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February 06, 2006 8:44 PM  
Blogger yhac said...

Did you mean p(A) or p(A|A)? How is either 0?

February 06, 2006 8:49 PM  
Blogger DhiOnlyOne said...

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.

February 07, 2006 7:18 PM  
Blogger eV said...

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.

February 08, 2006 12:26 AM  
Blogger madatadam said...

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.

February 08, 2006 1:11 PM  
Blogger DhiOnlyOne said...

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!

February 08, 2006 1:16 PM  
Blogger eV said...

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

February 08, 2006 6:38 PM  

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