Two customers (Customer #1 and Customer #2) just purchased identical insurance coverage. The number of claims for each insured is assumed to follow a Poisson distribution with mean 1.5 per year. Assume that the number of claims for Customer #1 is independent of the number of claims for Customer #2.
What is the probability that in the coming year, Customer #1 will have exactly one claim and Customer #2 will have exactly two claims?
The number of customers visiting a jewelry store on a weekday has a Poisson distribution with mean 4 per hour. Assume that for this jewelry store the number of customers in any given hour on a weekday is independent of the number of customers in any other hour on a weekday.
A prospective buyer of this jewelry store observes the business on a Wednesday for two one-hour periods (from 1 PM to 2 PM and 4 to 5 PM).
What is the probability that there will be 3 customers visiting from 1 PM to 2 PM and 5 customers visiting from 4 to 5 PM?