Your Practice Set – Applications and Interpretation for IBDP Mathematics
64
Paper 1 – Expected Value and Variance
Example
The random variable X is defined such that E ( X ) � 1.6 and Var ( X ) � 0.25 .
( a ) Find E ( 5� 4 X ).
( b ) Find Var ( 4 � 5 X ) .
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Another random variable Y is defined such that E ( Y) �� 0.8 . It is given that X and Y are independent .
[ 2 ]
( c ) Find E ( 3X
� 7 Y) .
[ 2 ]
Solution
( a ) E ( 5� 4 X) � 5� 4E ( X)
( b )
E ( 5� 4 X ) � 5� 4 ( 1.6 ) ( A1 ) for substitution
E ( 5�4 X ) � 11.4 A1
2
Var ( 4 �5 X) � ( � 5 ) Var ( X)
Var ( 4�5 X ) � ( 25 )( 0.25 ) ( A1 ) for substitution
Var ( 4�5 X ) � 6.25 A1
( c ) E ( 3X �7 Y) � 3E ( X ) � 7E ( Y)
E ( 3X
�7 Y) � 3 ( 1.6 ) �7 ( � 0.8 ) ( A1 ) for substitution
E ( 3X
�7 Y) � 10.4 A1
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