st371-20 joint rv 04

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 12 Outcome of each trial is exactly one of: , ,..., k E E E Probability of outcome is , 1,2,. .., where ... 1 jj 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 11 22 number of trials resulting in number of trials resulting in ... number of trials resulting in kk XE 12 Note that ... k X X X n
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(c) Tom Gerig ST371-20 joint rv 04 Page 4 Multinomial Distribution 12 The joint probability mass function for the s , ,..., is: k rv X X X 1 2 1 2 ( , ,..., ) ... , ,..., k x xx kk k n p x x x p p p x x x      where ... .
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st371-20 joint rv 04 - ST371 Distribution Theory...

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