Originally posted by twhitehead
From that link: The equation in the link simplifies for the special case in my OP problem because I am only interested here in the probability of there being NO event in that second. So, simplifying and adapting the equation in the link to my OP problem:”
P(X=0) = probability of a second interval having no event i.e. having 0 events.
e = Euler's number = 2.71828... (this is just the base of the natural logarithm )
then we simply have (for 0 events) :
P(X=0) = e ^ ( – F )
and, when I tried out a few F values, I always got results that intuitive seems very roughly about right so I am pretty sure I have got that right.
But, if I DID want to know the probability of there being a specific non-zero number of events in that second …....
For 1 event;
P(X=1) = F * e ^ ( – F )
For 2 events;
P(X=2) = ( (F^2) * e ^ ( – F ) ) / 2
For 3 events;
P(X=3) = ( (F^3) * e ^ ( – F ) ) / 6
For 4 events;
P(X=4) = ( (F^4) * e ^ ( – F ) ) / 24