is one chance in two that the estimate will be lower than 93% 
of the true value. 
The same example can be expressed in another way. Suppose 
that from the same fixed power spectrum a large number of different 
sections of 7) (t) are given, and suppose that the power in a given 
band is estimated for each of these sections. Then from this large 
number of estimates, the ratio of the number less than 32% of the 
true value to the total number will approach the fraction 1/40 as 
the total number of estimates is increased. Similar statements 
for each of the other values can be made. 
Thus for ten degrees of freedom, it is not possible to be 
very sure of the accuracy of one single estimate of the power in 
a given band. The value will be wrong by more than a factor of 
two one time out of ten. 
The error of a particular estimate 
Usually the true value of the power in the band under analy- 
sis is not known, and usually only one sample of 7(t) is avail- 
able. Thus only one estimate of the power in the band is avail- 
able and no additional analysis of the data can be carried out. 
The last table permits an interpretation of the accuracy of this 
one number. Thus, if UL from equation (10.32) is, say, ten 
thousand en*, then the true value of the power in the band will 
lie between twenty-six thousand em and five thousand five hundred 
cm? nine times out of ten for ten degrees of freedom. 
As the number of degrees of freedom is increased the range 
of values such that the true value will be included 90% of the 
time becomes smaller. For one hundred degrees of freedom, and 
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