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```Basic Concepts of Random Samples
Fundamental definitions from MCS 142:
“A simple random sample (SRS) of size n consists of n individuals from the population chosen
in such a way that every set of n individuals has an equal chance to be the sample actually
selected.”
“A probability sample is a sample chosen by chance. We must know what samples are possible
and what chance, or probability, each possible sample has.”
(Moore & McCabe, Introduction to the Practice of Statistics 4/e, Freeman, New York, 2003, p.
250).
The sample space S is our model of the population.
Row
Individual
X = weight
Y = height
1
s1
x1 = X(s1)
y1
2
s2
x2 = X(s2)
y2
3
s3
x3 = X(s3)
y3
n
sn
xn = X(sn)
yn
Other r.v.s
Notation: The upper-case letters X1, X2, X3, …, Xn denote random variables; Xj denotes a
numerical characteristic of the jth individual in the sample. We may view Xj as the “X”
characteristic of the jth individual sj : Xj = X(sj).
The lower-case letters x1, x2, x3, …, xn denote non-random numerical values of the
aforementioned random variables: xj = a numerical value of Xj.
An MCS-341, 342 definition: “Suppose that X1, X2, X3, …, Xn is an identically and
independently distributed (i.i.d.) sequence, i.e., X1, X2, …, Xn is a sample from some
distribution.” (Evans & Rosenthal, p. 199) In effect, the sample space S becomes the set of real
numbers, an infinite population, so this model is not suitable for samples from a finite
population, unless the population is large.
```