xuebaunion@vip.163.com

3551 Trousdale Rkwy, University Park, Los Angeles, CA

留学生论文指导和课程辅导

无忧GPA：https://www.essaygpa.com

工作时间：全年无休-早上8点到凌晨3点

微信客服：xiaoxionga100

微信客服：ITCS521

Assignment代写 - STAT 4004 Assignment 2

时间：2020-10-16

STAT 4004 Assignment 2 Due: October 19, 2020

1. Suppose the survivor function of the newborn lifetime T0 is given by

s(x) = exp

(

−

(

x

θ

)τ)

, x > 0

Find

(a) the density function of T0

(b) the hazard function of T0

(c) the probability that T0 is alive at 5 given T0 > 2

2. Suppose the survival function of the curtate lifetime of a newborn baby is given

by

s(x) =

100− x

100

, x = 0, 1, . . . , 100.

(a) the c.d.f. of K30

(b) the survival function of K30

(c) the probability mass function of K30

3. If lx = k(100− x)2 for 0 ≤ x ≤ 100, find

(a) 3p60

(b) 10|5q50

4. If K is the curtate future lifetime of (96), calculate Var(K), given the following

life table:

x 96 97 98 99 100

`x 180 130 73 31 0

5. A life at age 50 is subject to an extra hazard during the year of age 50 to 51.

If the standard probability of death from age 50 to 51 is 0.006, and if the extra

risk may be expressed by an addition to the standard force of mortality that

decreases uniformly from 0.03 at the beginning of the year to 0 at the end of

the year, calculate the probability that the life will survive to age 51.

6. From a life table with a one-year select period, you are given:

x `[x] d[x]

◦

e[x]

85 1000 100 5.556

86 850 100

Assume that deaths are uniformly distributed over each year of age. Calculate

◦

e[86].

7. Mr. Q Taro has only 3 hairs left on his head and he won’t be growing any more.

(a) The future mortality of each hair follows

k|qx = 0.1(k + 1), k = 0, 1, 2, 3 and x is Mr. Q Taro′s age

(b) Hair loss follows the uniform distribution of death assumption at fractional

ages.

(c) The future lifetime of 3 hairs are independent.

Calculate the probability that Mr. Q Taro is bald (has no hair left) at age

x+ 2.5.

8. Mortality for Don, aged 25, follows De Moivre’s law with ω = 100. If she

takes up hot air ballooning for the coming year, her assumed mortality will

be adjusted so that for the coming year only, she will have a constant force of

mortality of 0.1.

Calculate the decrease in the complete life expectancy for Don if she takes up

hot air ballooning.

9. For a ten-year select-and-ultimate table, you are given:

(a)

l[30]+t =

√

60

9

(

1− t

100

)

, 0 ≤ t < 10

(b)

l30+t =

√

70− t

10

, 10 ≤ t ≤ 70

Calculate

◦

e[30].

10. Show that

e

x:n =

n∑

k=1

kpx

where n is an integer.