[R] OT: distribution of a pathological random variate

[Horace Tso]

Folks,

I wonder if anything could be said about the distribution of a random variate x, where

x = N(0,1)/N(0,1)

Obviously x is pathological because it could be 0/0. If we exclude this point, so the set is {x/(0/0)}, does x have a well defined distribution? or does it exist a distribution that approximates x. 

(The case could be generalized of course to N(mu1, sigma1)/N(mu2, sigma2) and one still couldn't get away from the singularity.)

Any insight or reference to related discussion is appreciated.

Horace Tso