This post has no alternate problem. It has one problem with 2 parts.
A claim examiner of an insurer reviews the claim history of two independent insureds. Let be the annual number of claims of the first insured (Insured # 1). Let be the annual number of claims of the second insured (Insured # 2). The claim examiner finds tht follows a Poisson distribution with mean 1, and that follows a distribution with the following probability function.
- Between these two insureds, what is the probability that one of the insureds has two more claims than the other insured in a year?
- Given that one of the insured has two more claims than the other insured, what is the probability that Insured # 1 has more claims than Insured # 2?