Hello tutors. Kindly solve the following questions. Remember to include explanations for ease in understanding.

Given the following select and ultimate mortality rates from AF80, construct the corresponding ly 's for ages x from 45 and 46. Age Duration 0 Duration 1 Duration 2+ 45 0.000838 46 0.000924 0.001158 47 0.001018 0.001284 0.001415 48 0.001423 0.001564 49 0.001729The numbers of claims made last year by individual motor insurance policyholders were: Number of claims 0 2 3 4+ Number of policyholders 2.962 382 47 25 Carry out a chi square test to determine whether these frequencies can be considered to conform to a Poisson distribution.Consider the following lifetime optimal consumption-saving problem T MAX B' Inc (11) subject to It1 = R(a-0).1=0. .. ..T (12) 0 = 0(0). ar+120, (13) where 8 is the consumer's rate of time preference (8