On Wednesday, 24 April 2013 at 10:46:57 UTC, Andrea Fontana wrote:
What's the probability to guess a precise number in [0..1]? I
think is 0 as long as you have infinite numbers.
Right.
What's the probability to guess a interval in [0..1]? I think
it's the interval size.
Right again.
I mean that a random real number is not valid mathematically
too. In any given real interval there are infinite numbers, how
you can choose a number in an infinite (and non-numerable!)
interval? I think you always need some sampling.
Am I wrong?
In a sense, yes. A continuous probability distribution is
well-defined. In short, as you pointed out, you can coherently
define the probabilities to hit each possible segment and get a
useful mathematical object, though the probability to hit each
single point is zero. It's no less strict than a typical high
school definition of an integral. See the link for more info:
http://en.wikipedia.org/wiki/Probability_distribution#Continuous_probability_distribution
.
