Assignment 1 solution unstarred

# Assignment 1 solution unstarred - of students spent less...

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THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT0301 Elementary Statistical Methods Semester 1 2009/2010 Assignment 1 solution ( questions that no need to hand in)

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7. Let A and B the principal amounts for fund A and fund B respectively, i.e. A = \$2.5 m , B = \$1.2 m and n = 7 Let X A and X B be the final values for fund A and fund B respectively. X A = 2.5 ( 1 + 0.105 )( 1 + 0.20 )( 1 + 0.078 )( 1 0.03 )( 1 + 0.082 )( 1 + 0.012 )( 1 0.041 ) = 3.63999183 X B = 1.2 ( 1 + 0.184 )( 1 + 0.135 )( 1 0.104 )( 1 0.058 )( 1 0.192 )( 1 + 0.037 )( 1 + 0.09 ) = 1.243095051 Let r be the average annual growth rate, then we have (A+B) )( 1 + r ) 7 =X A +X B ∴( 2.5 + 1.2 )( 1 + r ) 7 = 3.63999183 + 1.243095051 r = 4.043% 8. Please see Tutorial solutions for question #8.

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12. (a) Mean = 4E(X) – 13 = 207 Median = Median (U) = 4Med(X) – 13 = 215 Mode = Mod(U) = 4Mode(U) – 13 = 219 Variance = 16Var(X) = 784 Stdev = Variance 0.5 = 28