3. Let's say we are doing pet insurance. The survivalship of a population of pets is such that 20% fail during the first 5 years, with the age at failure uniformly distributed. After that, they are subject to a constant force of mortality so that at age x = 10, there are only 10% left. The force of interest is d 5%. a) Find the APV of a whole life policy for a 2-year-old pet that pays $5000 at the time of death. Include in your answer the notation for this value. b) Find the APV of a term life policy of 6 years on a 2 year-old pet that pays $5000 at the time of death if death occurs before age 8. Include in your answer the notation for this value. c) Find $5000 * 6E2. Explain in words what this is. d) Find Var(Z2), where Z2) is the present value random variable for a whole life policy for a 2 year-old pet that pays $5000 at the time of death. (to ensure that you compute your survival function accurately, check that the probability of surviving to age 8 is 23%). 3. Let's say we are doing pet insurance. The survivalship of a population of pets is such that 20% fail during the first 5 years, with the age at failure uniformly distributed. After that, they are subject to a constant force of mortality so that at age x = 10, there are only 10% left. The force of interest is d 5%. a) Find the APV of a whole life policy for a 2-year-old pet that pays $5000 at the time of death. Include in your answer the notation for this value. b) Find the APV of a term life policy of 6 years on a 2 year-old pet that pays $5000 at the time of death if death occurs before age 8. Include in your answer the notation for this value. c) Find $5000 * 6E2. Explain in words what this is. d) Find Var(Z2), where Z2) is the present value random variable for a whole life policy for a 2 year-old pet that pays $5000 at the time of death. (to ensure that you compute your survival function accurately, check that the probability of surviving to age 8 is 23%)