See,
~:10'1\
'S,So
52
I.
Random Sample
Y\
population 
N
'I.
l
:.
~\..(,
\J~
\
l,\
e
Of
\
~O..Yr\f
sample·
"observed values
of
a sequence
of
random variables" 
n
I
~A.Def
If
each
of
the samples has an equal probability
of
being
selected, the sampling
is
said to be random and the result
is
said to
be
a random sample (RS).
1.
X
1
, ••• ,
X
0
r.v.'s constitute a RS
of
size n
if
the Xi's are independent
and have the same prob. dist. That is,
if
they are independent and
identically dist. (iid).

 ~

,
2.
IfX
1
,
••.
,~is
a RS, then for
Xi~(μ,
cr
2
),
Ll
e1V\
'i~
Cul
..;
,
•
xi
~
(μ,
cr
2
),
i
=
1,
...
, n
·>
..h'
:.
t
et'
1
t
V'iD~
\1'1\ta.r\~
,
.)
1
'
l
'b~CAM~e •
Cov(Xi, Xj)
=
0,
i
*
j.
\JJ
V\t
'<'t
E;,
::.
,·+"'
('tJ..
't\
tiVV\
'(C.\O.,
'f
u,.
\
I
d ,.
.
.

X ·
X
,
ev,o..
t\\l
\fl
~'<"t>'M
JV.
W\'r
½
t_
QI/\~

'
Q'f~
\V\<}._~~~eJ...eV\~·
e"
\Vl,t\9
.
l
I.
Linear
om 1nation
\
(
0
,
/J )
'1
t~
~A.
Def
1.
Conditions: X
1
, ••• ,
X
0
are n r.v.'s and a
1
, ••• ,
a
0
are n constants.
n
2.
+
a X
= "
a.
X.
is
a linear combination
of
nn
11
i=l
the X's.
B. Expected Value:
n
n
n
E[Y]
=
E[L
aiXJ
=
L
aiE[XJ
=
L
i=l
i=l
i=l