This preview shows pages 1–5. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: m wax Name:
I.D.: UNIVERSITY OF WATERLOO
DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE
MIDTERM TEST #4 ACTUARIAL SCIENCE 331, SPRING 2004 EXAMINER: H.H. PANJER TIME: 80 minutes QUESTION AVAILABLE MARK » $1" 1. A multiple decrement table with 2 causes of death has the joint p.d.f. 0.03+0.002t, 0<t$10, j=1
f(t,j)= 0.04+0.004t, O<t$10, j=2 0, otherwise
Find: (a) The marginal distribution of the time to death.
(b) The marginal distribution of the cause of death. (c) The distribution of the time to death if it is known that J = 1. (d) The probability that J = 1, if it is know that T = 5. 3
2. A triple—decrement service table has the following entries at age 3::
1
g) = 0.06
9 = 0.12
9) = 0.03
Where (1) refers to death, (2) refers to disability and (3) refers to re
tirement. a , ( 3
Em
Find the probabilities of death, disability and retirement in the as
sociated single decrement tables. Assume that each decrement has a
constant force over the one—year interval (as, x + 1] CW.“ {wit ! new ,jﬂ‘fy :: {if} “vi"‘3’
. J;
l . 51 j ’ ' J. a {W
l  g 1 .l 3. You are given the following information for a person age :13: i) The probability of death in the next year in the associated sin gle decrement mortality table is 0.20. Deaths are uniformly dis— tributed , oughout the year. 1 ‘ ii) Ignoring death (i.e. in the associated single decrement table) the A ,9. 4., r; W probability of retirement in the next year is 0.30. Half of retire
merits occur wayxthrough the year. The remainder occur at
‘ 73.?” .  ’7? 7 ‘~.
2" ’ year end: Find: (a) The probability that the person remains active at age :1: + 1. (b) The probability that the person dies while in service before age
a: + 1 (c) The probability that the person retires before or at age as + 1. iii; 1 4. A Whole life insurance policy issued to (x) pays $1000 only on accidental death. Assume: «‘g. i) a force of accidental death of .005 for all ages. ' <1 "“ " ""
ii) a force of nonaccidental death of .015 for all ages. ; 2 ;; iii) a force of interest of .050. :: gm ‘17 (a) Find the net annual (fully continuous) premium for this policy. (b) If death occurs at age a: + t, what is the probability that it was accidental? (c) If is alive in 10 years, What is the reserve at age a: + 10? PM i
l
a 5 , a M
{r} ‘5 g g” UHKW , A"
a is:
. 2t
~ '4: M” H ‘ 4 ' 0‘0
4:4,; 3 5’ [MN 1? r M 1 ' ,
/ F
"in p 12‘ I 1“? l
l  ? i u . J 40‘
m r "J 43"]. l "’0'; 5 f I “0‘1,” g,» u .. uni—Mr ' _..—
i( 0“ J a l (I W \  b.1337 :1 0 0‘; J ) ’3 9 E 9W” ( 9) u"? L 7 a "m? [L
)I} ‘ \~ 1., ’ a
w ~ w w 4 ~ ., "w .
on 4 ,1 Db, V Anal ‘ rqlﬁ , V,
.a a V , _.  DA
1:1,}: ‘“ jai L: 4 4* a e, a « I .u 90} 1 £3 0 u? ...
View Full
Document
 Spring '09
 david

Click to edit the document details