st371-20 joint rv 04 - ST371 Distribution Theory...

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(c) Tom Gerig ST371-20 joint rv 04 Page 1 ST371 Introduction to Probability and Distribution Theory Joint Probability Distributions: Multinomial Distribution
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(c) Tom Gerig ST371-20 joint rv 04 Page 2 Multinomial Experiment indentical and repeatable trials n 1 2 Outcome of each trial is exactly one of: , ,..., k E E E 1 2 Probability of outcome is , 1,2,..., where ... 1 j j k E p j k p p p Trials are independent The following structure defin Multinomial Experim es a ent :
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(c) Tom Gerig ST371-20 joint rv 04 Page 3 Having performed a multinomial experiment, define the (discrete) random variables: k Multinomial Random Variables 1 1 2 2 number of trials resulting in number of trials resulting in ... number of trials resulting in k k X E X E X E 1 2 Note that ... k X X X n
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(c) Tom Gerig ST371-20 joint rv 04 Page 4 Multinomial Distribution 1 2 The joint probability mass function for the s , ,..., is: k rv X X X 1 2 1 2 1 2 1 2 ( , ,..., ) ...
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