131A_1_Lecture_4-1_Winter_2012

# 131A_1_Lecture_4-1_Winter_2012 - EE 131A Probability...

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UCLA EE131A (KY) 1 EE 131A Probability Professor Kung Yao Electrical Engineering Department University of California, Los Angeles Lecture 4-1

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UCLA EE131A (KY) 2 Discrete sample space (1) Suppose the sample space S = {a 1 , …, a n } is finite. Then each outcome in the sample space is called an elementary event . All elementary events are mutually exclusive (disjoint). Ex. 1. Let B be an event of S with B = {a 1 , a 4 , a 5 }, then P( B ) = P(a 1 ) + P(a 4 ) + P(a 5 ) . In general, let . (In Ex. 1. k 1 = 1, k 2 = 4, and k 3 = 5.) Thus,   12 m kk k a, a , , a B i m k i=1 P( ) = P(a ) . B
UCLA EE131A (KY) 3 Discrete sample space (2) Consider a discrete sample space with n elements S = {a 1 , a 2 , …, a n }. The experiment is said be equally likely outcomes if P(a 1 ) = P(a 2 ) = … = P(a n ) = 1/n . Ex. 2. For a “fair” die, S = {1, 2, …, 6} and P(“1”) = P(“2”) = … = P(“6”) = 1/6 . In an equally likely outcome exp., if an event B = {a 1 , a 4 , a 5 }, then 145 3 P(B) = P(a ) P(a ) P(a ) . n 

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UCLA EE131A (KY) 4 Discrete sample space (3) Ex. 3. If a “fair” die is tossed, let B = {Outcome is less or equal to 4} = {“1”, “2”, “3”, “4”}. Then P( B ) = 4/ 6 = 2/3 . Ex. 4. An urn has 10 balls with S = {0, 1, 2, …, 9}. In an exp., pick one ball randomly and notes its number. A = {Number is odd} = {1, 3, 5, 7, 9}. B = {A positive no. and a multiple of 3} = {3, 6, 9}. C = {Number is less than 5} = {0, 1, 2, 3, 4}.
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## This note was uploaded on 02/29/2012 for the course ELECTRICAL 131a taught by Professor Yao during the Spring '12 term at UCLA.

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131A_1_Lecture_4-1_Winter_2012 - EE 131A Probability...

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