
Mathematical Ideas (13th Edition) - Standalone book
13th Edition
ISBN: 9780321977076
Author: Charles D. Miller, Vern E. Heeren, John Hornsby, Christopher Heeren
Publisher: PEARSON
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Question
Chapter 12.1, Problem 35E
(a)
To determine
An empirical probability distribution just for the vowels A, E, I, O, and U from the distribution table provided mentioned below.
Letter
Probability
Letter
Probability
E
0.130
L
0.035
T
0.090
C, M, U
0.030
A, O
0.080
F, P, Y
0.020
N
0.070
W, G, B
0.015
I, R
0.065
V
0.010
S, H
0.060
K, X, J
0.005
D
0.040
Q, Z
0.002
Letter | Probability | Letter | Probability | |
E | 0.130 | L | 0.035 | |
T | 0.090 | C, M, U | 0.030 | |
A, O | 0.080 | F, P, Y | 0.020 | |
N | 0.070 | W, G, B | 0.015 | |
I, R | 0.065 | V | 0.010 | |
S, H | 0.060 | K, X, J | 0.005 | |
D | 0.040 | Q, Z | 0.002 |
(b)
To determine
To graph: An appropriately labeled bar graph from the distribution constructed in part (a) if the empirical probability distribution just for the vowels is as follows:
Vowel | Probability |
A | 0.208 |
E | 0.337 |
I | 0.169 |
O | 0.207 |
U | 0.077 |
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9.22 Develop, debug, and test a program in either a high-level language or a macro
language of your choice to solve a system of equations with Gauss-Jordan elimination
without partial pivoting. Base the program on the pseudocode from Fig. 9.10. Test the
program using the same system as in Prob. 9.18. Compute the total number of flops in
your algorithm to verify Eq. 9.37.
FIGURE 9.10
Pseudocode to implement the
Gauss-Jordan algorithm with-
out partial pivoting.
SUB GaussJordan(aug, m, n, x)
DOFOR k = 1, m
d = aug(k, k)
DOFOR j = 1, n
aug(k, j) = aug(k, j)/d
END DO
DOFOR 1 = 1, m
IF 1 % K THEN
d = aug(i, k)
DOFOR j = k, n
aug(1, j)
END DO
aug(1, j) - d*aug(k, j)
END IF
END DO
END DO
DOFOR k = 1, m
x(k) = aug(k, n)
END DO
END GaussJordan
11.9 Recall from Prob. 10.8, that the following system of equations
is designed to determine concentrations (the e's in g/m³) in a series
of coupled reactors as a function of amount of mass input to each
reactor (the right-hand sides are in g/day):
15c3cc33300
-3c18c26c3 = 1200
-4c₁₂+12c3 = 2400
Solve this problem with the Gauss-Seidel method to & = 5%.
9.8 Given the equations
10x+2x2-x3 = 27
-3x-6x2+2x3 = -61.5
x1 + x2 + 5x3 = -21.5
(a) Solve by naive Gauss elimination. Show all steps of the compu-
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Chapter 12 Solutions
Mathematical Ideas (13th Edition) - Standalone book
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