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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
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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 μ = Z 1 x (3 x 2 )d x = 3 x 4 4 ¯ ¯ ¯ ¯ 1 = 3 4 and σ 2 = Z 1 ( x − 3 / 4) 2 (3 x 2 )d x = 0 . 0375 . 97...
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