Question:
The number of accidents follows a Poisson distribution with mean 12. Each accident generates 1, 2 or 3 claimants with probabilities 1/6,1/3,1/2, respectively.
Calculate the probability that there are at most 3 claimants.
Attempt:
E(N) = 12[\frac{1}{6}+2*\frac{1}{3}+3*\frac{1}{2}]...