Expected
Value of a
Sample
Estimate
\f ~B7tf'-
Statistical Reporting Service • U.S.Department of Agriculture. SRS No.19
)
r
Z
'
)
FOREWORD
The Statistical
Reporting Service (SRS) has been engaged for
manyyears
in the training of agricultural
statisticians
from around
the world. Most of these participants
comeunder the support of the .
.Agency for International
Development (AID) training programs; however,
many also comeunder sponsorship of the Food and Agr1cul,tur~.~.rganization
I
.'
"
r'
,I
~
..
into
the International
Statistical
Programs Center of the Bureau of the
Census, with which SRSis c·ooperating.
This treatise was developed by the SRSwith the .cooperation of .
AIDand the Center,
in an effort
to provide improved materials
for.
"'
"
,~
teaching and reference
in the area of agricultural
statistics,
not
only for foreign students but also for ~evelopment of staff working
for these agencies.
..!~~
.,
.....
",
,,_I
\
I,
\,)t
Washington, D. C.
i
HARRY C. TRELOGAN
Administrator
Statistical
Reporting Service
September 1974
~ I~~: ..~~'.
,",
~,:;jt::~~.0~
.
"
" ~ • 1.~;"••
PREFACE
The author has felt
that applied courses in s~lin~
should give more
attention
to elementary theory of expected values of a random variable.
The theory .pertaining
to a 'random variable
and to functions of random
variables
is
the foundation for probability
sampling.
Interpretations
of the accuracy of estimates
from probability
sample surveys are predicated
on, amongother
things,
the theory of expected values.
There are many students with career
interests
in surveys and the
application
of probability
sampli~g who have very limited backgrounds in
mathematics and statistics.
Training in sampling should go beyond simply
..
in mathematics and -probability
should be included.
It can (1) add 'mU:ch'
learning about sample designs in a descriptive manner.
••
I
h ••
~
The foundations
-,
.
•
!..·I
"
to the breadth of understanding of bias,
random sampling error,
components'
,
'
of error,
and other
technical
concepts;
(2) enhance one's ability
to make