is t.he same as in example 6.16.
Denoting HJ - HG by [!H, the
existing condition can be written as:
After reformulation we get:
be easily written in the matrix form as
B = [1, 1, 1],
7. Consider problem number 1 of this exercise.
Assume that the observed
and 8 have got also non-random (systematic) errors of
-1 em and 5" respectively.
derived height h
Compute the expected total error in the
8. Determine t
whose elements have large numerical values.
The d.evelopment of these
formulae is done analogically to the formulation of equations (4.20),
(4.22), (4.25) and (4.26).
Here we state only the results, and the
elaboration is left to the student.
= Ls !/.,!/.,
Here we have to require again that
i.e. that both components of
the multisample have the same number of elements (see section 3.3.5).
Obviously, if this requirement is satisfied for all the p
truncation by 8
and the error due to rounding by 8
[-0.5 10-n, 0.5 10-n)
and we may postulate that-8
has a parent random variable distributed
according to the rectangular (uniform) PDF (see section 3.2.5)
and by applyi.ng the covariance law (equation ( 6.15 ) we
[s; ab] a/d
Let us assume that the primary multisample L
we have dealt with in Examples 6.1 and 6.3 is give
From equations (5-9) ' ( 5-10) and (5-ll) we get:
28* 2 i=l
The condition (5-9) can be then rewritten as:
From equation (5-5), we have:
and we get
Consequently, the variance cr , or rather the standard deviation cr
be considered the only parameter of G.
Substituting equation (4-8) into
equation (4-4) we get
The range, Ra(t;) of the sample t;: (C , i=l,2, . n) is defined
as the difference between the largest (t;9;l and the smallest (F;s) elements
Consequently, for an ascendingly ordered sample t;, we get
In technical practice, as well as in all experimental sciences,
one is faced with the following problem:
evaluate quantitatively para-
meters describing properties, features, relations or behaviour of various
objects around us.
(compound) probability of A and B, that is
and B, and known as the combined
Similarly, we define the combined probability of occurrence of
the independent D1 , D2'
Dnc: D as the product of their individual
PDF (see 3.1.2) of a random sample.
From our abstract experiment it
can be seen that
( 3 .15)
since the area under the "smooth histogram" must again equal to 1 (see
This is the third property of a PDF, the integrability and
Let us determine the covariances between the different
pairs of components of the multisample n given in example 3.20.
The covariances 8jk are computed from equation (3-54 as follows:
= 8 21 = 5
[(-2)(3) + (-1)(1) + (0)(-3) +