st371-21 fns of rv 01

st371-21 fns of rv 01 - ST371 Introduction to Probability...

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(c) Tom Gerig ST371-21 fns of rv 01 Page 1 ST371 Introduction to Probability and Distribution Theory Joint Probability Distributions: Linear Combinations
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(c) Tom Gerig ST371-21 fns of rv 01 Page 2 1 2 1 2 Let , , ..., be s and , , ... be numerical constants. Then the statistic nn X X X n rv a a a n Linear Combinations 1 1 2 2 ... Y a X a X a X 12 linear combinat is called a io of ,, n . ( ., . ) . n LC X X X
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(c) Tom Gerig ST371-21 fns of rv 01 Page 3 Examples of linear combinations are: 12 1 and 1 aa   Mean of , ,..., : n X X X Y X X  1 ... n a a a n ( ... )/ n Y X X X n Differences between s , : rv X X Linear Combinations
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(c) Tom Gerig ST371-21 fns of rv 01 Page 4 1 2 1 2 Let , , ..., be s and , , ... be numerical constants. Suppose that nn X X X n rv a a a n 2 ( ) and ( ) , 1, 2,. .., i i i i E X V X i n  and let 1 1 2 2 ... Y a X a X a X Linear Combinations
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(c) Tom Gerig ST371-21 fns of rv 01 Page 5 12 1 1 2 2 1 1 2 2 : For any , , ... Theorem ,: ( ) ( ... ) ... n nn X X X E Y E a X a X a X a a a Linear Combinations
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(c) Tom Gerig ST371-21 fns of rv 01 Page 6 Examples: 1 2 1 2 () E X X  12 ( ) ( ...
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st371-21 fns of rv 01 - ST371 Introduction to Probability...

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