Only b)

1. For a portfolio of 1800 insurance risks: (i) Each risk can be classified as good or bad. (ii) There are twice as many good risks as there are bad risks. (iii) Each good risk has a claim count that follows a negative binomial distribution with r = 1 and B = 0.4. (iv) Each bad risk has a claim count that follows a negative binomial distribution with r = 2 and 3 = 1. (a) Calculate the probability that a risk randomly selected from the port- folio has exactly one claim. (b) Calculate the variance of the number of claims (N) using the law of total variance by conditioning on Class (which can be either good or bad) as follows: Var(N) = E[Var(N|Class)] + Var[E(N|Class)]. Note there are two possible values for E(N|Class), and two possible values for Var(N|Class). You must use the law of total variance to earn credit for this question. 1. For a portfolio of 1800 insurance risks: (i) Each risk can be classified as good or bad. (ii) There are twice as many good risks as there are bad risks. (iii) Each good risk has a claim count that follows a negative binomial distribution with r = 1 and B = 0.4. (iv) Each bad risk has a claim count that follows a negative binomial distribution with r = 2 and 3 = 1. (a) Calculate the probability that a risk randomly selected from the port- folio has exactly one claim. (b) Calculate the variance of the number of claims (N) using the law of total variance by conditioning on Class (which can be either good or bad) as follows: Var(N) = E[Var(N|Class)] + Var[E(N|Class)]. Note there are two possible values for E(N|Class), and two possible values for Var(N|Class). You must use the law of total variance to earn credit for this