Your question doesn't really make sense as is.
Hi stats guys,
I had a heated discussion about the following situation today:
Let’s say I have a function f(x) producing values between 0 and 1, then I can consider this as a probability. If I have a function g(x) producing values between 0 and 0.5, is this still a probability, since values large than 0.5 could never be achieved?
Thanks!
Your question doesn't really make sense as is.
I don't have emotions and sometimes that makes me very sad.
Well if you really want to interpret the output as a probability then you can do that. Still doesn't necessarily make sense and we wouldn't call it a probability function unless it met other criteria as well.
I don't have emotions and sometimes that makes me very sad.
Okay thanks for your answer but could you please be more detailed. Sorry that I repeat my question again:
I am not talking about a PDF (with unity of the integral etc), simply a mechanism (whatever it is) producing values from 0 to 1. To my understanding this output could be considered as a probability, right? If I now modify this function to produce only values from 0 to 0.5, is this is still a probability even values from (0.5,1] never occur.
It would be just about as much as a "probability" as the outputs from the other function.
I don't have emotions and sometimes that makes me very sad.
To check whether something is a valid probability, you look at the probability axioms and see if they are really satisfied.
http://en.wikipedia.org/wiki/Probability_axioms
One thing to note that is . If your arbitrary function never map to the value , then it cannot be a probability.
Put it in other words: In the probability axioms, there is no requirement that the probability must be a surjective function - as you seen from those simple discrete probability models. However it does require it to map to the values as is the trival -algebra over any sample space.
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