Explain probability of some buses with Poisson process

Question

Explain probability of some buses having arrived when the Poisson process is utilized.

Answer 1

If the Poisson process is utilized to model events, like the arrival of buses at a bus-stop, then we can respond questions about the number of buses arriving along with an exact time using the result as follows:

P(q(t) = n) = e^-λt(λt)ⁿ/n!.

It is the probability of exactly n buses having arrived or there having been n asset price jumps in a time t.