Re: random partition an exponential distributed interval

From: Markus Triska (triska_at_gmx.at)
Date: 06/30/04 

Date: Wed, 30 Jun 2004 16:00:48 +0200

> I met a problem which can be expressed as that given an interval,
> which lenght L are exponential random variable and its probability
> dense function is lampda * exp(-lampda * x), we partition the interval
> into pieces. These pieces' lengths are i.i.d random variables, then
> the number of the pieces is a random variable with geometric
> distribution, how to prove it?

If I understood you correctly and only the length of the original
interval is exponentially distributed, with no prerequisites about the
pieces, then this is not generally true - it depends on how you
partition the interval. For example, you could decide to make only one
piece: the interval itself. The number N of pieces would then follow a
Dirac distribution (P(N = 1) = 1, P(N != 1) = 0).

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