12 . The following table shows the probability distribution of a discrete random variable X .
x |
3 |
5 |
7 |
9 |
|
P (
X
� x)
|
0.3 |
0.1 |
0.15 |
0.45 |
( a ) Find E ( X ) .
[ 2 ] Another random variable Y is defined such that E ( Y) � 17 and Var ( Y) � 3. It is given that X and Y are independent , and Var ( X ) � 6.75 .
( b ) |
Find E (
2X
�
5 Y)
.
|
( c ) |
Find Var (
2X
�
5 Y)
.
|
[ 2 ]
[ 2 ]
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