Chapter5NEWSolutions

Chapter5NEWSolutions - Chapter 5 5.1 Lets use Fnn and Mnn...

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Chapter 5 5.1 Let’s use F nn and M nn to represent the events “A female lives to age nn .” and similar for a Male. a) If a female lives to 50, what is the probability she lives to 80 can be written P(F80|F50) = ) 50 ( ) 80 50 ( F P F F P . Now notice that the set A80 = {F | F lives to be 80} is a subset of the set A50 defined in a similar way – that is to say that if you live to be 80 then you also lived to be 50, so the probability of being in A80 and A50 is the same as the probability of being in A80. Then our expression becomes: 623 . 0 955 . 0 595 . 0 ) 50 ( ) 80 ( = = = F P F P . For F90 the analysis is similar giving us 251 . 0 955 . 0 240 . 0 ) 50 ( ) 90 ( ) 50 | 90 ( = = = F P F P F F P . For males the numbers are 408 . 0 920 . 0 375 . 0 ) 50 ( ) 80 ( ) 50 | 80 ( = = = M P M P M M P and P(M90|M50) = 103 . 0 920 . 0 095 . 0 = b) This is just the fraction of the population each group is multiplied by their probability of living to 90: (0.51)(.095) + (0.49)(.240) = 0.167 or 16.7% 5.2 F(x) = 1 – 2 -x x = 0,1,2,… a) First, note that f(0) = 0. Then for x = 1,2,… f(x) = F(x) – F(x-1) = 1 – 2 -(x) – (1 – 2 -(x-1) ) = 2 -x (-1 +2) = 2 -x b) P(X = 5) = f(5) = 2 -5 = 0.03125 P(X 5) = 1 – P(X < 5) = 1 – (0 + 0.5 + 0.25 + 0.125 + 0.0625) = 0.0625 Alternately, P(X 5) = P(X = 5) + P(X = 6) + … = 2 -5 + 2 -6 +2 -7 +… = 2 -5 (1 + ½ + ¼ + …) which you recognize as a geometric series with a = 2 -5 and r = 0.5 = 0625 . 0 2 5 . 0 1 2 4 5 = =
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5.3 a) Notice that order does not matter here, since distinguishing between first and second
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This note was uploaded on 11/30/2010 for the course MATH 235/237 taught by Professor Wilkie during the Spring '10 term at Waterloo.

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Chapter5NEWSolutions - Chapter 5 5.1 Lets use Fnn and Mnn...

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