Re: Conditional Probability Mass Functions

In article <2e601517-a999-493f-b9b2-47791c688d0e@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Randy Poe <poespam-trap@xxxxxxxxx> wrote:
On Dec 10, 12:45 pm, RalphLeon <rgoo...@xxxxxxxxx> wrote:
Hi folks,

Is it possible to condition a discrete random variable with a
continuous one?

For example the parameter of a Poisson distribution being a RV from a
uniform distribution?

The book I'm using treats both cases separately and says nothing about
a mixture of the two types....

They're probably trying to keep the mathematics
elementary, so you either see either ordinary Riemann
integrals or sums.

However, if you use Stieltjes integrals instead
of Riemann integrals, for instance defining expectation
of f(x) as integral(-inf,inf) f(x) dP(x) where P(x)
is the cumulative distribution, then you can state
general results that handle discrete, continuous, or
mixed distributions, and still keep things pretty elementary.

Ross (_A First Course in Probability_) takes this
approach.

Stieltjes introduces the Stieljes integral because
measure theory had not yet been invented, and he
was working on the moment problem (using cumulative
distribution functions).

--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@xxxxxxxxxxxxxxx Phone: (765)494-6054 FAX: (765)494-0558
.

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