4.6

by hand

2004-05-23, 2023-03-12

d_0,1 = d_0,1 = 0.950
d_0,2 = d_0,1 * d_1,2 = 0.950 * 0.940 = 0.893
d_0,3 = d_0,2 * d_2,3 = 0.940 * 0.932 = 0.832
d_0,4 = d_0,3 * d_3,4 = 0.932 * 0.925 = 0.770
d_0,5 = d_0,4 * d_4,5 = 0.925 * 0.919 = 0.708
d_0,6 = d_0,5 * d_5,6 = 0.919 * 0.913 = 0.646

Python

added on 2015-04-11, revise on 2023-03-12.

code

# 4.6.py
# 2023/03/12
  
# initialize d
d = [[0 for i in range(6+1)] for j in range(5+1)]
  
# input
d[0][1] = 0.950
d[1][2] = 0.940
d[2][3] = 0.932
d[3][4] = 0.925
d[4][5] = 0.919
d[5][6] = 0.913
  
print("4.6.py")
print("given data")
for i in range(len(d)):
    print(d[i])
  
# calculation
  
# d[0][1] = d[0][1]
# d[0][2] = d[0][1] * d[1][2]
# d[0][3] = d[0][1] * d[1][2] * d[2][3]
# d[0][4] = d[0][1] * d[1][2] * d[2][3] * d[3][4]
# d[0][5] = d[0][1] * d[1][2] * d[2][3] * d[3][4] * d[4][5]
# d[0][6] = d[0][1] * d[1][2] * d[2][3] * d[3][4] * d[4][5] * d[5][6]
  
#for j in [1,2,3,4,5,6]:
for j in range(1, len(d)+1):
    z = 1
    for k in range(0, j):
        z *= d[k][k+1]
    d[0][j] = z
  
# output
print("given data")
for i in range(len(d)):
    print("d[{:d}, {:d}]= {:.3f}".format(i, i+1, d[i][i+1]))
  
print("answer")
for j in range(1, len(d)+1):
    print("d[0, {:d}]= {:.3f}".format(j, d[0][j]))
  
print("list d")
for i in range(len(d)):
    print("".join("{:6.3f}".format(element) for element in d[i]))
# end of code

output

4.6.py
given data
[0, 0.95, 0, 0, 0, 0, 0]
[0, 0, 0.94, 0, 0, 0, 0]
[0, 0, 0, 0.932, 0, 0, 0]
[0, 0, 0, 0, 0.925, 0, 0]
[0, 0, 0, 0, 0, 0.919, 0]
[0, 0, 0, 0, 0, 0, 0.913]
given data
d[0, 1]= 0.950
d[1, 2]= 0.940
d[2, 3]= 0.932
d[3, 4]= 0.925
d[4, 5]= 0.919
d[5, 6]= 0.913
answer
d[0, 1]= 0.950
d[0, 2]= 0.893
d[0, 3]= 0.832
d[0, 4]= 0.770
d[0, 5]= 0.707
d[0, 6]= 0.646
list d
 0.000 0.950 0.893 0.832 0.770 0.707 0.646
 0.000 0.000 0.940 0.000 0.000 0.000 0.000
 0.000 0.000 0.000 0.932 0.000 0.000 0.000
 0.000 0.000 0.000 0.000 0.925 0.000 0.000
 0.000 0.000 0.000 0.000 0.000 0.919 0.000
 0.000 0.000 0.000 0.000 0.000 0.000 0.913

history

2004-05-23 create.
2015-04-11 add Python code.
2023-03-12 revise Python code.