131A_1_Lecture14-2_Winter_2012

131A_1_Lecture14-2_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 14-2
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UCLA EE131A (KY) 2 Randomness of a sequence of numbers (1) Introduction - Given a sequence of numbers, how can we tell if it is random? Ex. 1. Given {4, 14, 23, 34}, can we “predict” the next integer? No, the next number is “42”, since these numbers are the North-South subway train station in NYC. Clearly, this sequence of no. is not random. Suppose we toss a coin and denote an “1” for a “head” and “0” for a “tail.” Then the i-th rv X i has the sample space S = {0, 1}. If given a sequence of 1’s and 0’s, from the toss of a coin, why do we believe the outcomes are “random?” In other words, what characterizes a “random sequence?”
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UCLA EE131A (KY) 3 Randomness of a sequence of numbers (2) Given a coin toss of length n, we can find P(“1”) and P(“0”) by using P(“1”) = Number of “1” s / n, P(“0”) = Number of “0” s / n. The coin is “fair” if P(“1”) = P(“0”) = 1/2. In other words, we use the “relative frequency concept”
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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_Lecture14-2_Winter_2012 - EE 131A Probability...

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