Re: Probability Problem 2

Topi Linkala wrote:
Let's take the following function:

x < 0 f=0
0 <= x <= 1 f=1
1 < x f=0

Any integral from x to x of f is zero but integral from 0 to 1 is 1.

If you think I don't recognize this, you're not demonstrating good
reading skills.

What you give is a perfectly good uniform pdf over the interval [0, 1].
However, the poster is looking for a uniform pdf over the entire reals
R, not just some interval within R. Such a pdf of course does not
exist. In my original post, I said this imprecisely by saying that
you can't sum up a bunch of zeros to get zero. In my response to Mark
Tilford (I think it was him), I made this more precise by stating that
you can't integrate a function that is constantly zero everywhere and
get anything but zero.

If this is taken as a probability function then each real value of x has
probablity of zero. The propabilities of reals less than 0,5 is 0,5 etc.

The pdf is not the probability function in the sense that f(x) is the
probability of getting x. The pdf is the probability density function
at x--that is, the limit of the probability of selecting a number in
the interval [x, x+dx], divided by dx, as dx approaches zero.

I notice You keep putting little cute comments in your signature, as
though I misunderstood infinite cardinalities, instead of simply having
been imprecise in my original statement.

Actually, your last comment is somewhat imprecise, too. The
cardinality of the reals is not defined to be aleph-one. It is really
axiomatic: It is undecidable within ZFC. See "continuum hypothesis."
See how easy it is to nitpick about facets that have nothing to do with
the topic? :)

I certainly hope you do not disagree that there are no uniform
probability distributions over the entire reals--the main point of my
posts.

--
Brian Tung <brian@xxxxxxx>
The Astronomy Corner at http://astro.isi.edu/
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.

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