代做ACTU PS5821 Actuarial Methods - Autumn 2024 Assignment - 4代做留学生SQL语言程序

ACTU PS5821 Actuarial Methods - Autumn 2024

Assignment - 4

Assigned 9/27/24, Due 10/5/24

Problem  1.   A population consists of 30% smokers with µx   =  0.2 and 70% non-smokers with µx  = 0.1.  Calculate the 75th percentile of a randomly selected individual’s future timelife random variable.

Problem 2.  Calculate the complete expectation of life at age 40 if you are given the following. 40p0  = 0.6, E(T0 ) = 62 and E[min(T0 , t)] = t − 0.005t2 , 0 < t < 60.

Problem 3.

Consider a select-ultimate survival model with a 2-year select period, where

µ [37]+t  = µ37+t  A, 0 2

Find the value of A if you are given the following.

˚(e)[37]  = 58,     ˚(e)37  = 57.5,     ˚(e)[37]: 2  = 1.9,     ˚(e)37: 2  = 1.7

Problem 4. The force of mortality for a life selected at age x is

µ [x]+t  = (β + 0.006S + 0.003x)t, t > 0

where where S = 1 if (x) smokes and S = 0 otherwise. Also, 10p[3(n)0(o)n]smoker  = 0.96

(a) Find the value of β

(b) Calculate the probability that a life randomly drawn from a population of lives selected at age

30 of which 40% are smokers, will survive at least 10 years.

Problem  5.   T20   follows a uniform distribution with a limiting age of 120.   Find n such that˚(e)20: ni = 48

 

 

 

 


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