5.57 Mortgage companies sometimes have customers default on their loans. To understand the effect that it can have on the company, they often model the risk of default. In the reduced form model of...

Extracted text: 5.57 Mortgage companies sometimes have customers default on their loans. To understand the effect that it can have on the company, they often model the risk of default. In the reduced form model of credit risk, it is assumed that defaults occur according to a Poisson process with a mean of per year. For a particular company, A = 10; that is, on average 10 customers default each year. What is the probability that the firm will have more than eight defaults in a given year? b What is the probability that the firm will have no defaults during a given year? Given that there has been no default in the first half of the year, what is the probability that there will be at least eight this year?