131A_1_Lecture_5-1_Winter_2012

# 131A_1_Lecture_5-1_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 5-1

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UCLA EE131A (KY) 2 Independence of Events (1) Consider two events A and B . If the occurrence of event B does not affect the probability of event A , then A and B are independent . Formally, the independence of A and B is given by P( A ) = P( A | B ) = P( A B ) / P( B ) . (1) Equivalently, P( A ) P( B ) = P( A B ) . (2) But P( A B ) = P( B | A ) P( A ) . (3) Equating the r.h.s. of (2) to the l.h.s. of (3), yields P( A ) P( B ) = P( B | A ) P( A ) or P( B ) = P( B | A ) . (4)
UCLA EE131A (KY) 3 Independence of Events (2) The concept of independence of two events is intuitively clear in some simple experiences and not so obvious in more complex situations. Consider a random experiment in which we flip a coin and also toss a die, from the physics of the situation, we believe the output of the coin is independent of the outcome of the die (to be confirmed in Ex. 1.) On the other hand, the av. weight of the corn at harvest time in Iowa and the av. amount of rainfall in the last three months before harvesting in Iowa are probably not independent (needs a lot of statistical data to confirm this conjecture).

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UCLA EE131A (KY) 4 Independence of Events (3) From (1), (2), and (4) of page 2, formally the independence of
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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_5-1_Winter_2012 - EE 131A Probability...

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