Question

Poisson Distribution:
A small life insurance company has determined that on the average it receives 3 death claims per day. Find the probability that the company receives at least four death claims on a randomly selected day.

Answer 1

for mean m
\[P(n=i) = \frac{e^{-m} m^i} {i!}\]
we have m = 3, we want P(i > 4)
a bit of a pain
\[e^{-3} \approx 0.05\]
P(n=0) = 0.05
P(n=1) = 0.05 x 3 / 1
P(n=2) = 0.05 x 9 / 2
P(n=3) = 0.05 x 27 / 6

Answer 2

I forgot to include n=4. Calculate the five terms, add them together, and subtract them from 1.