ans to prob1

ans to prob1 - Suggested Answer to ECON 346 Problem Set 1...

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1 Suggested Answer to ECON 346 Problem Set 1 #1 (a) - (b) P ( X i ) Probability; CD ( X i ) Cumulative distribution Mean: = = = 8 1 ) ( ] [ i i i i X P X X E μ Median: the middle point of the data, that is, the point at the cumulative distribution = 0.5 Variance: = - = - = 8 1 2 2 2 ) ( ) ( ] ) [( i i i i X P X X E σ Standard deviation: 01836 . 0 000337 . 0 2 = = = Table 1 X i P ( X i ) CD ( X i ) X i · P ( X i ) ( Xi - μ ) 2 ( Xi - μ ) 2 · P ( X i ) 0.05 0.04 0.04 0.002 0.00142884 0.00005715 0.06 0.06 0.10 0.0036 0.00077284 0.00004637 0.07 0.16 0.26 0.0112 0.00031684 0.00005069 0.08 0.22 0.48 0.0176 0.000061 0.00001338 0.09 0.14 0.62 0.0126 0.000005 0.00000068 0.10 0.18 0.80 0.018 0.00014884 0.00002679 0.11 0.12 0.92 0.0132 0.00049284 0.00005914 0.12 0.08 1.00 0.0096 0.00103684 0.00008295 Summation 1.00 0.0878 ( Mean ) 0.00426272 0.000337 ( Variance ) (c) Table 2 X i X i + 100 X i · 100 P ( X i ) X i · P ( X i ) [ X i + 100 ] · P ( X i ) [ X i · 100 ] · P ( X i ) 0.05 100.05 5 0.04 0.002 4.002 0.2 0.06 100.06 6 0.06 0.0036 6.0036 0.36 0.07 100.07 7 0.16 0.0112 16.0112 1.12 0.08 100.08 8 0.22 0.0176 22.0176 1.76 0.09 100.09 9 0.14 0.0126 14.0126 1.26 0.1 100.1 10 0.18 0.018 18.018 1.8 0.11 100.11 11 0.12 0.0132 12.0132 1.32 0.12 100.12 12 0.08 0.0096 8.0096 0.96 Summation 1.00 0.0878 ( μ Xi ) 100.0878 ( μ Xi+100 ) 8.78 ( μ Xi*100 ) According to Table 2 above, we can find: 0878 . 0 ) ( = = Xi i X E 0878 . 100 ) 100 ( 100 = = + + Xi i X E 78 . 8 ) 100 * ( 100 * = = Xi i X E
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2 So, we can prove the following relationship: ) ( 100 0878 . 0 100 0878 . 100 ) 100 ( i i X E X E + = + = = + ) ( * 100 0878 . 0 * 100 78 . 8 ) 100 * ( i i X E X E = = = (d) Table 3 X i P ( X i ) X i + 100 X i · 100 ( Xi+100 - μ Xi+100 ) 2 [( Xi+100 - μ Xi+100 ) 2 ] · P ( X i ) ( Xi · 100 - μ Xi
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ans to prob1 - Suggested Answer to ECON 346 Problem Set 1...

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