131A_1_Wed2_4_2_08

131A_1_Wed2_4_2_08 - EE 131A Probability Professor Kung Yao...

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UCLA EE131A (KY) 1 EE 131A Probability Professor Kung Yao Electrical Engineering Department University of California, Los Angeles Samplings Wed. April 2, 2008
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UCLA EE131A (KY) 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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UCLA EE131A (KY) 3 Sampling (2) Method 1-Sampling 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 k-tuple given by . Since each element of this k-tuple can be any one of the n possible element of S, then the total number of distinct ordered k-tuple, N k = n x n x …n = n k . 12 (, , , ) k xx x = x "
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UCLA EE131A (KY) 4 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 2-tuple = 4 2 = 16 .
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UCLA EE131A (KY) 5 Sampling (4) Ex. 2. S = {1, 2, 3, 4, 5}, n = 5, k = 2.
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131A_1_Wed2_4_2_08 - EE 131A Probability Professor Kung Yao...

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