Apps. and Interpretation for IBDP Maths Ebook 2 | Page 257

15
Exercise 67
1 . The following table shows the probability distribution of a discrete random variable X .
x
2
4
6
8
P ( X � x)
0.6
0.1
0.15
0.15
( a ) Find E ( X ) .
[ 2 ]
Another random variable Y is defined such that E ( Y) � 10 and Var ( Y) � 2 . It is given that X and Y are independent , and Var ( X ) � 5.31 .

15

( b )
Find E (
5X �
2 Y)
.
( c )
Find Var (
5X �
2 Y)
.
[ 2 ]
[ 2 ]
2 . The random variable X is defined such that X ~ B ( 100 , 0.65 ) .
( a ) Find E ( X ) .
( b ) Find Var ( X ) .
[ 2 ]
Another random variable Y is defined such that E ( Y) � 30 and Var ( Y) � 7 . It is given that X and Y are independent .
[ 2 ]
( c )
Find E (
2X �
7 Y)
.
( d )
Find Var (
2X �
7 Y)
.
[ 2 ]
[ 2 ]
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