Exercise 64
1 . The random variable X is defined such that E ( X ) � 21.5 and Var ( X ) � 3.
( a ) Find E ( 1� 10 X ) .
( b ) Find Var ( 5� 2 X ) .
Another random variable Y is defined such that E ( Y) � 20 . It is given that X and Y are independent .
( c ) Find E ( 5�4X
� 3 Y) .
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2 . The random variable X is defined such that E ( 5 X ) � 40 and Var ( 1�2 X ) � 4.
( a ) Find E ( X ) .
( b ) Find Var ( X ) .
Another random variable Y is defined such that E ( Y) � 20 . It is given that X and Y are independent .
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( c ) Find E ( �X
� Y) .
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3 . The random variable X is defined such that E ( X ) �� 5 and Var ( X ) � 16 .
( a ) Find E ( 100 � X ).
( b ) Find Var ( 99 � 5 X ) .
Another random variable Y is defined such that Var ( Y) � 8. It is given that X and Y are independent .
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( c ) Find Var ( 6X
� 5 Y) .
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