Re: Questions about probability functions

In article <1150134980.041285.96370@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Zerex71 <mfeher@xxxxxxxxxxx> wrote:

Robert Israel wrote:
Zerex71 wrote:

2. Why wouldn't a random distribution simply be a flat line of some
value Y over a defined interval [a,b]? In other words, why would it be
a bell curve when there is equal likelihood that a random value will be
selected over the range [a,b] -- wouldn't any draw from the interval be
equally likely to occur and thus there would be no slope? (This is
just something I was pondering recently.)

If the distribution is uniform on the interval [a,b], in the sense that
the
probabilities of different sub-intervals of the same length are always
equal,
then indeed it is not a bell curve: the density of the uniform
distribution on the
interval [a,b] is constant on that interval. The "bell curve" is for a
normal
distribution.

So what would you call a non-bell curve distribution? The picture I
have in
my head is, one decides that a probability problem can be represented
in
terms of a flat line of constant value Y across the interval [a,b] and
zero outside
of it.

In this case you'd call it a uniform distribution on the interval
[a,b].

In other words, all outcomes are equally likely (discrete or
continuous, I suppose,
it doesn't matter to me).

But it does matter to me. This is a continuous distribution, and for
any continuous distribution all individual outcomes have probability 0.
So "all outcomes are equally likely" is not useful here.

Robert Israel israel@xxxxxxxxxxx
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
.

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