Sampling distributions and
point estimators
By Gözdem Dural Selçuk

Definitions
•
The random variables
X
1
,
X
2
,…,
X
n
are a
random sample
of size
n
if:
a)
The
X
i
‘s are independent random variables.
b)
Every
X
i
has the same probability distribution.
•
A
statistic
is any function of the observations in a random sample.
•
The probability distribution of a statistic is called a
sampling
distribution
.

Numerical Summaries of Data
•
Data are the numeric observations of a phenomenon of interest.
The
totality of all observations is a
population
.
A portion used for analysis
is a random
sample
.
•
We gain an understanding of this collection, possibly massive, by
describing it numerically and graphically, usually with the sample
data.
•
We describe the collection in terms of shape, outliers, center, and
spread (SOCS).
•
The center is measured by the mean.
•
The spread is measured by the variance.

Fig_6-3
Relationship between a population and a sample

Sample Mean