Differential Equations Solutions 87

Differential Equations Solutions 87 - 5 . 6) 2 + (5 5 . 6)...

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Chapter 16 Solutions: Monte Carlo Principles CHALLENGE 16.1. The mean is the sum of the samples divided by the number of samples: μ 6 =24 / 6 = 4. The variance is σ 2 6 = 1 6 £ (1 4) 2 +(2 4) 2 +(5 4) 2 +(8 4) 2 +(6 4) 2 +(2 4) 2 ¤ = 19 3 . CHALLENGE 16.2. The probability of drawing each card is 1 / 10, so the mean of the distribution is μ = 1 10 (1+2+3+4+5+6+7+8+10+10)=5 . 6 . The variance is σ 2 = 1 10 £ (1 5 . 6) 2 +(2 5 . 6) 2 +(3 5 . 6) 2 +(4
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Unformatted text preview: 5 . 6) 2 + (5 5 . 6) 2 + (6 5 . 6) 2 +(7 5 . 6) 2 + (8 5 . 6) 2 + (10 5 . 6) 2 + (10 5 . 6) 2 = 9 . 04 . CHALLENGE 16.3. Clearly f ( x ) 0, and Z 1 3 x 2 d x = x 3 1 = 1 . We calculate = Z 1 x (3 x 2 )d x = 3 x 4 4 1 = 3 4 and 2 = Z 1 ( x 3 / 4) 2 (3 x 2 )d x = 0 . 0375 . 97...
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This note was uploaded on 01/21/2012 for the course MAP 3302 taught by Professor Dr.robin during the Fall '11 term at University of Florida.

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