Survey sampling

Survey sampling

\(\bullet\)What is survey sampling?(c.f.census survey)(c.f.:参考，查看，来源于拉丁语)
\(\bullet\)understanding the whole by a \(\underline{fraction}\)(i.e.a \(\underline{sample}\))
Population:
Q:What is the population to survey?(In some cases,it can be difficult to identify or determine)
N:population size
a sample of size n:a subgroup of n members(n<N)
Q:Which n members should be included in the sample?(i.e.how to produce a \(\underline{representative}\) sample)
quantity of interest:
\(x_i,i=1,2,3\cdots N\)(each labeled by an integer)
\(x_i\)can be \(\underline{numerical}\) or \(\underline{categorial}\)
Multivariate\((x_{i1},x_{i2}\cdots x_{ik}),i=1,2,3 \dots N\)
\(\underline{Definition : }\)(survey sampling)
A technique to obtain \(\underline{information}\) about a \(\underline{large}\) population by examining only