Fax nightmares: Poisson distributions and conditional probabilities

Last night, I had a dream that I had a notice on my answering machine with instructions on how to deliver a fax. As it turns out, I have not had a fax machine connected to my phone for many years now and, now that I think about it, although I have sent a handful of faxes during the last year, I am not sure that I have actually received a fax at work during the last six months (or during the last year, for that matter). Anyway, the message set to press some buttons (as one would do to use a fax on a shared voice phoneline), but somehow, I did not have a fax connected. So far as I recall, it wasn't that I was actually expecting any faxes, but it appears that I heard the answering macine go off. (These days, I give out my more permanent cell phone number rather than my home phone, so there is usually no reason for me to answer the phone at home--statistically, it is very likely to be a wrong number or a "spam" call).

Does it take an eccentric to have a nightmare about fax machines? It probably doesn't. These things are probably a very rare event that happens with the same limited frequency among eccentrics, "normal" people, and "others." That is, the null hypothesis that the conditional probability is the same for all three groups is probably the same. The event probably follows a Poisson Distribution.