Question 3. You are conducting a long-term investigation into the mortality of a group of genetically modified rodents that are thought to have a life span of around 10 years. The experiment involves observing tenidentical rodents until they reach an age of 10 years exact. The below table summarizes the results; it gives the age at which they first enter the investigation, the age at which they leave, and the reason fordeparture. Rodent 1 2345678 Entry age (years) 1 Exit age (years) 9 3/12 Reason died 2/12 10 survived to the end 3 2/12 10 survived to the end 2 7/12 4 escaped 0 2 5/12 died 0 9 11/12 died 1 9/12 10 survived to the end 3 4/12 1 5/12 8 3/12 6 escaped died 7 10 9 10 survived to the end (a) [5 marks] Define the actuarial estimate of the probability of a new-born rodent dying within 10years and calculate it. (b) [5 marks] Write down the likelihood under a Poisson model, assuming that the force of mortality isconstant over the 10 years. Hence derive the Poisson estimate of the probability of the new-born rodentdying within 10 years.