# Hw07ans - STAT 408 Spring 2009 Homework#7(due Friday March...

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STAT 408 Spring 2009 Homework #7 (due Friday, March 13, by 3:00 p.m.) 1. A simple model for describing mortality in the general population in a particular country is given by the probability density function ( 29 ( 29 2 6 18 100 10 252 y y y f - = , 0 < y < 100. a) Verify that f ( y ) is a valid probability density function. 1. f ( y ) 0 for each y ; checkbld 2. ( 29 1 = - y y f d . ( 29 ( 29 ( 29 - = - = - 1 0 2 6 100 0 2 6 18 1 252 100 10 252 x x x y y y y y f d d d = 504 2 252 0 1 9 1 8 1 2 7 1 252 9 8 7 = + - x x x = 1. checkbld b) Based on this model, which event is more likely or A: a person dies between the ages of 70 and 80 B: a person lives past age 80? A: ( 29 ( 29 - = - 8 . 0 7 . 0 2 6 80 70 2 6 18 1 252 100 10 252 x x x y y y d d = 7 . 0 8 . 0 9 1 8 1 2 7 1 252 9 8 7 + - x x x 0.7382 – 0.4628 = 0.2754 .

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B: ( 29 ( 29 - = - 0 . 1 8 . 0 2 6 100 80 2 6 18 1 252 100 10 252 x x x y y y d d = 8 . 0 0 . 1 9 1 8 1 2 7 1 252 9 8 7 + - x x x 1 – 0.7382 = 0.2618 . A is more likely. c) Given that a randomly selected individual just celebrated his 60th birthday, find the probability that he will live past age 80. P ( over 80 | over 60 ) = ( ( 29 60 over P 60 over 80 over P = ( 29 ( 29 - - 100 60 2 6 18 100 80 2 6 18 100 10 252 100 10 252 y y y y y y d d 2318 . 0 1 7382 . 0 1 - - = 7682 . 0 0.2618 0.3408 . d) Find the value of y that maximizes f ( y ) ( mode ). f ' ( y )

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