{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

RelativeResourceManager

# RelativeResourceManager - (ii The probability that two...

This preview shows pages 1–5. Sign up to view the full content.

MATH 471: Actuarial Theory I Homework #1: Fall 2009 Assigned August 26, due September 2 1. If F ( x ) = x 110 for 0 x 110 (de Moivre’s Law), find expressions for the following; where 0 x 110 for (a) – (b), and 0 t 70 for (c) – (e): (a) f ( x ) (b) s ( x ) (c) t p 40 (d) t q 40 (e) the p.d.f. of T(40) 2. Let s ( x ) = ( 100 100+ x ) 2 for x 0. Calculate: (a) The probability that (25) will survive at least 40 more years. (0.5739) (b) The probability that (30) will die within the next 20 years. (0.2489) (c) The probability that (35) will die between ages 45 and 60. (0.1549) 3. You are given the following information: (i) The probability that two 70-year olds are both alive in 20 years is 0.16.

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

View Full Document

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: (ii) The probability that two 80-year olds are both alive in 20 years is 0.01. (iii) There is an 8% chance of a 70-year old surviving the next 30 years. (iv) All lives are independent and have the same expected mortality. Calculate the probability that an 80-year old will survive to age 90. (0.5) 4. Suppose mortality follows modiﬁed (or generalized) de Moivre’s Law , where: s ( x ) = ( ω-x ω ) α for 0 ≤ x ≤ ω , α > 0. Note that regular de Moivre’s Law is a special case of this modiﬁed law with α = 1. Show that: t p x = ( ω-x-t ω-x ) α for 0 ≤ t ≤ ( ω-x ), α > 0....
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