Lecture_3-1_July_2010

Lecture_3-1_July_2010 - EE 131A Probability Professor Kung...

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UCLA EE131A (KY) 1 EE 131A Probability Professor Kung Yao Electrical Engineering Department University of California, Los Angeles M.S. On-Line Engineering Program Lecture 3 - 1
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UCLA EE131A (KY) 2 Lecture 3 -1: More on counting (1) General Principle of Counting The most general principle of counting in k experiments follows: Suppose the first exp. has: n 1 possible outcomes; The second exp. has: n 2 possible outcomes; The k-th exp. has: n k possible outcomes. The total number of possible outcomes is given by N k = n 1 x n 2 x …x n k. (1)
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UCLA EE131A (KY) 3 We note, if n 1 = n 2 = … = n k = n, then (1) show N k = n x n x …x n = n k , (2) which is equivalent to the result of Method 1 (Sampling with replacement and with ordering) Ex. 1. Suppose you have 4 shirts and 3 pants. How many possible outfits can you have? Let n 1 = 4 and n 2 =3. Then with k = 2, we have N 2 = 4 x 3 = 12 different possible outfits. Ex. 2. Consider a three-wheel “combination lock” in which the first wheel has 10 digits, the second has 9 digits, and the third has 8 digits. This lock has N 3 = 10 x 9 x 8 = 720 possible realizations. More on counting (2)
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UCLA EE131A (KY) 4 Examples using different sampling methods (1) Ex. 1. Consider all airports identified by three letters from the English alphabet with 26 letters (e.g., LAX).
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Lecture_3-1_July_2010 - EE 131A Probability Professor Kung...

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