Your Practice Set – Applications and Interpretation for IBDP Mathematics
67
Paper 1 – General Problems
Example |
The following table shows the probability distribution of a discrete random variable X . |
x |
10 |
20 |
30 |
40 |
P ( X � x) |
0.1 |
0.3 |
0.5 |
0.1 |
( a ) Find E ( X ) .
[ 2 ]
Another random variable Y is defined such that E ( Y) �Var ( Y) � 15 . It is given that X and Y are independent , and Var ( X ) � 64 .
( b ) |
Find E ( X �
Y)
.
|
( c ) |
Find Var (
3X �
7 Y)
.
|
[ 2 ]
[ 2 ]
Solution
( a ) E ( X ) � ( 10 )( 0.1 ) � ( 20 )( 0.3 ) � ( 30 )( 0.5 ) � ( 40 )( 0.1 ) ( A1 ) for substitution E ( X ) � 26
A1
( b ) E ( X �Y) � E ( X ) � E ( Y)
( c )
E ( X �Y) � 26 � 15
( A1 ) for substitution
E ( X �Y) � 41
A1
2 2
Var ( 3X � 7 Y) � 3 Var ( X ) � 7 Var ( Y)
Var ( 3X
� 7 Y) � 9 ( 64 ) � 49 ( 15 ) ( A1 ) for substitution
Var ( 3X
�7 Y) � 1311 A1
[ 2 ]
[ 2 ]
[ 2 ]
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