Say I have a nonbias die with sides
1-200. Let X be the r.v counting the number of times
200 is rolled out of
500 trials. So, $X \approx bin(500,0.005)$.
How can one change this problem such that we actually need a poisson distribution to model the probability situation? What is the random variable whose distribution I'm looking at? How will the poisson distribution also be looking at the probability of success? I simply don't know how to create an analogy between it and the binomial distribution.
[Note: I am aware that the poisson distribution can be used to approximate the binomial distribution in scenarios such as the one pointed out above, since the number of trials and the probability of success is quite small. However, this is not my question.]
Someone please help.