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
Unformatted text preview: AMS 410 Actuarial Mathematics Fall 2009 Exam 1 Solution September 24, 2009 Answers: V1: ECDAB EADCD V2: DACCD EEEDA 1. A doctor is studying the relationship between high blood pressure and heartbeat abnormalities in her patients. She tests a random sample of her patients and nds that: 40% have high blood pressure; of those with high blood pressure, 60% have an irregular heartbeat; of those with an irregular heartbeat, 80% have high blood pressure. For a randomly chosen person, What portion of the patients selected have an irregular heartbeat? Answer: 30% De ne events : H=high blood pressure, I=irregular heartbeat. P [ H ] = 40% , P [ I  H ] = 60% , thus P [ I H ] = P [ H ] P [ I  H ] = 24% ; P [ H  I ] = P [ I H ] P [ I ] = 24% P [ I ] = 80% , thus P [ I ] = 30% . 2. An insurance agent o ers his clients auto insurance, homeowners insurance and life insurance. The purchases of the three products are mutuall y independent . The pro le of the agent's clients is as follows: 55% of the clients have auto insurance; 45% of the clients have homeowners insurance; 60% of the clients have life insurance. Calculate the percentage of the agent's clients that have more than one insurance product. Answer: 55 De ne three events as A, H and L. P [ A ] = 55% , P [ H ] = 45% , P [ L ] = 60% . The required probability is N 4 + N 5 + N 6 + N 7 = P [ A H L ]+ P [ A H L ]+ P [ A H L ]+ P [ A H L ] . Since the three events are mutually independent, P [ A H L ] = 0 . 55 . 45 (1 . 6) = 0 . 099 , P [ A H L ] = (1 . 55) . 45 . 6 = 0 . 1215 , P [ A H L ] = 0 . 55...
View
Full
Document
This note was uploaded on 08/08/2010 for the course AMS 410 taught by Professor Yang,y during the Fall '08 term at SUNY Stony Brook.
 Fall '08
 Yang,Y

Click to edit the document details