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exam mlc nov 2005 solutions

# exam mlc nov 2005 solutions - Fall 2005 Exam M Solutions...

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Fall 2005 Exam M Solutions Question #1 Key: C [ ] [ ] 2 2 Var Z E Z E Z = [ ] ( ) ( ) ( ) 0.08 0.03 0.02 0 0 0.02 t t t t t t x x E Z v b p t dt e e e dt µ = = ( ) 0.07 0 0.02 2 0.02 7 0.07 t e dt = = = ( ) ( ) ( ) ( ) 2 2 2 0.05 0.02 0 0 0.02 t t t t t x x E Z v b p t dt e e dt µ = = ( ) 0.12 0 2 1 0.02 12 6 t x e t dt µ = = = [ ] ( ) 2 1 1 4 2 0.08503 7 6 6 49 Var Z = = = Question #2 Key: C From 1 x A dax = ±± we have ( ) 0.1 3 1 8 11 1.1 x A = = ( ) 10 0.1 5 1 6 11 1.1 x A + = = x x i A A δ = × ( ) ( ) 10 3 0.1 0.2861 11 ln 1.1 5 0.1 0.4769 11 ln 1.1 x x A A + = × = = × = ( ) 10 10 10 x x x x V A P A a + + = × ±± 0.2861 0.4769 6 8 = = 0.2623 There are many other equivalent formulas that could be used.

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