15
15
Linear Combinations
of Variables
SUMMARY POINTs
� Properties of linear transformations of independent random variables : 1 . E ( aX �b) � aE ( X ) � b 2 .
2
Var ( aX �b) � a Var ( X ) 3 . E ( a1 X1 � a2 X
2
� � a X ) � a1E ( X1) � a2E ( X
2) � � a E ( X )
4 . n n n n
Var ( a X � a X � � a X ) � a Var ( X ) � a Var ( X ) � � a Var ( X )
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Solutions of Chapter 15
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