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UCLA
EE131A (KY)
1
EE 131A
Probability
Professor Kung Yao
Electrical Engineering Department
University of California, Los Angeles
M.S. OnLine Engineering Program
Lecture 2  2
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EE131A (KY)
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Lecture 2 2:
Sampling (1)
•
There are four basic methods
of sampling
(picking)
k objects out of a set of n distinct objects
.
•
Each sampling method can be performed with
replacement
or without replacement.
•
Furthermore, results of these two sampling methods
can be tabulated with ordering
or without ordering
.
•
Sampling
With Replacement
Without Replacement
With Ordering
Without Ordering
With Ordering
Without Ordering
Method 1
Method 4
Method 2
Method 3
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EE131A (KY)
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Sampling (2)
Method 1Sampling with Replacement and with
Ordering
A set S has
n distinct objects
.
Pick any one
object randomly and note its identity on an
ordered list
, and
return
that object back to the
set. Perform this operation
k times
. Denote the
outcomes in the ordered list as an ktuple given
by
.
Since each element of this ktuple can be any
one of the
n possible element of S, then the total
number of distinct ordered ktuple,
N
k
= n x n x …n = n
k
.
12
(,
,
,
)
k
xx
x
x
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Sampling (3)
Ex. 1.
S
= {a, b, c, d}, n = 4, k = 2.
abc
d
a
(a,a)
(a,b)
(a,c)
(a,d)
b
(b,a)
(b,b)
(b,c)
(b,d)
c
(c,a)
(c,b)
(c,c)
(c,d)
d
(d,a)
(d,b)
(d,c)
(d,d)
Table 1.
Realizations of 2 objects taken from a set of 4
distinct objects with ordering.
Total no. of distinct 2tuple = 4
2
= 16 .
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EE131A (KY)
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Sampling (4)
Ex. 2.
S
= {1, 2, 3, 4, 5}, n = 5, k = 2.
Table 2.
Realizations of 2 objects taken from a set of 5
distinct objects with ordering.
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This note was uploaded on 10/27/2010 for the course EE 131A 19062528 taught by Professor Kungyao during the Fall '10 term at UCLA.
 Fall '10
 KungYao

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