Mathematic Methods HW Solutions 70

Mathematic Methods HW Solutions 70 - . 263 8.3 = 0, 2 =...

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Chapter 15 70 4.9 25 / 102, 25 / 77, 49 / 101, 12 / 25 4.11 0 . 097, 0 . 37, 0 . 67; 13 4.12 5 4.14 n ! /n n 4.17 MB: 16, FD: 6, BE: 10 4.18 MB: 125, FD: 10, BE: 35 4.21 C ( n + 2 ,n ) 4.22 0 . 135 4.23 0 . 30 5.1 μ = 0, σ = 3 5.2 μ = 7, σ = r 35 / 6 5.3 μ = 2, σ = 2 5.4 μ = 1, σ = 21 / 2 5.5 μ = 1, σ = r 7 / 6 5.6 μ = 3, σ = r 284 / 13 = 4 . 67 5.7 μ = 3(2 p - 1), σ = 2 r 3 p (1 - p ) 5.8 E ( x ) = $12 . 25 5.12 E ( x ) = 7 5.15 ¯ x = 3(2 p - 1) 5.17 Problem 5.2: E ( x 2 ) = 329 / 6, σ 2 = 35 / 6 Problem 5.6: E ( x 2 ) = 401 / 13, σ 2 = 284 / 13 Problem 5.7: E ( x 2 ) = 24 p 2 - 24 p + 9, σ 2 = 12 p (1 - p ) 6.1 (a) f ( x ) = π - 1 ( a 2 - x 2 ) - 1 / 2 (c) ¯ x = 0, σ = a/ 2 6.2 e - 2 = 0 . 135 6.3 f ( h ) = 1 / (2 l l - h ) 6.4 f ( x ) = αe - α 2 x 2 / π , ¯ x = 0, σ = 1 / ( α 2 ) 6.5 f ( t ) = λe - λt , F ( t ) = 1 - e - λt , ¯ t = 1 , half life = ¯ t ln 2 6.6 F ( r ) = r 2 , f ( r ) = 2 r , ¯ r = 2 / 3, σ = 2 / 6 6.7 (a) F ( s ) = 2[1 - cos( s/R )], f ( s ) = (2 /R ) sin( s/R ) (b) F ( s ) = [1 - cos( s/R )] / [1 - cos(1 /R )] = s 2 , f ( s ) = R - 1 [1 - cos(1 /R )] - 1 sin( s/R ) = 2 s 6.8 f ( r ) = 3 r 2 ; ¯ r = 3 / 4, σ = r 3 / 80 = 0 . 19 6.9 f ( r ) = 4 a - 3 r 2 e - 2 r/a n Exactly 7 h At most 7 h At least 7 h Most probable number of h Expected number of h 7.1 7 0 . 0078 1 0 . 0078 3 or 4 7 / 2 7.2 12 0 . 193 0 . 806 0 . 387 6 6 7.3 15 0 . 196 0 . 500 0 . 696 7 or 8 15 / 2 7.4 18 0 . 121 0 . 240 0 . 881 9 9 7.5
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Unformatted text preview: . 263 8.3 = 0, 2 = kT/m , f ( v ) = 1 r 2 kT/m e-mv 2 / (2 kT ) In (8.11) to (8.20), the rst number is the binomial result and the second number is the normal approximation using whole steps at the ends as in Example 2. 8.11 0 . 0796, 0 . 0798 8.12 0 . 03987, 0 . 03989 8.13 0 . 9598, 0 . 9596 8.14 0 . 9546, 0 . 9546 8.15 0 . 03520, 0 . 03521 8.16 0 . 4176, 0 . 4177 8.17 0 . 0770, 0 . 0782 8.18 0 . 372, 0 . 376 8.19 0 . 0946, 0 . 0967 8.20 0 . 462, 0 . 455 8.25 C: 38 . 3%, B and D: 24 . 2%, A and F: 6 . 7% In + 1 2 and + 3 2 , change 1 2 to 0 . 5244, and 3 2 to 1 . 2816....
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