# old8 - UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN Actuarial...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN Actuarial Science Program DEPARTMENT OF MATHEMATICS Math 478 / 568 Prof. Rick Gorvett Actuarial Modeling Spring, 2011 Old Actuarial Exam Problems Kernel Estimators (1) You are given the following ages at time of death for 10 individuals: 4 _> {MFmtcA-L 90MB. 0? 25 30 55 35 37 39 45 47 49 55 - you: 931.: 7’0. Using a uniform kernel with bandwidth b = 10, determine the kernel density estimate of the probability of survR/al to age 40. '0 8 ‘ Ans-n: PMﬂoﬂmoH A.» .} _ [than ‘63) (A)0.377 X 83:!) 7V0 >q° -Q"‘°p° ) (B) 0.400 g} 25--“ . zr .01.? (C) 0.417 m“ zr-vr nu" .eﬂ" (D) 0439 3? 2.9—4? .3! .031" @0485 39 2.4 “(a .qr .o'u" ‘16!“ 3r—J'f . or (Sample Questions, Exam C, Problem # 268) 4 394') , n- MA“ ” 3" “"7 . 9r «:3:- rr VI-sr' I as ' ° 7 r ‘ ' ' °° ’7. 424’ (2) From a population having distribution function F, you are given the following sample: e‘nﬂmmc ﬂeas, 3F (Ac-u 2.0, 3.3, 3.3, 4.0, 4.0, 4.7, 4.7, 4.7 _ ¢ — /: Calculate the kernel density estimate of F (4), using the uniform kernel with bandwidth 1.4 ' “”6‘ Hormonal r“ 3' it 7": 7.4:. X t 5 .o o B: _ (A) 0.31 ———-— M ___f___‘!‘:—9———- 5’ 14:1. (B) 0.41 2.0 94"“ Lee .12.: l .ur (C) 0.50 3,3 [.9 - ‘0) 6.95“ ‘3‘; .m’lf 7- .137! .53 4° 1.5-535! are .062! Z .214“ )0.63 4“, 3.3 - 6.1 0.2.r .oanr 3 .oqaqr ' (Sample Questions, Exam C, Problem # 1 4 7) ﬂ (3) You study ﬁve lives to estimate the time from the onset of a disease to death. The times to death are: ‘ 2 3 3 3 7 }) ‘9 PMB.“ EACH. J' Using a triangular kernel with bandwidth 2, estimate the density function at 2.5. b = 2. """' (A) 8/40 2/40 2‘5: 2 = (0.53 4.5-) ) 14/40 (D) 16/40 (B) 17/40 =7 Fir-n ‘7’ or f 08:. mm. cwmisure (Sample Questions, Exam C, Problem # 3) To P093- @ 1.5‘. I HG‘IGH‘?’ = lzJ Junce’ 1 .1 :- 35 (4)0451“) ...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern