Analysis and Approaches for IBDP Maths Ebook 2 | Page 246

Your Practice Set – Analysis and Approaches for IBDP Mathematics
3. The following table shows the probability distribution of a discrete random variable X .
x � 2 0 2 4
P( X � x)
2
r � 0.21 r 0.25 0.15
(a) Find the value of r .
(b) Find E( X ) .
Another discrete random variable Y is defined by Y �aX � b , a , b�
that Var( X ) � 4.35 , Var( Y) � 17.4 and E( Y) � 5.5 .
�
[2]
[2]
. It is also given
(c) Find the value of a .
(d) Write down the value of b .
[2]
[1]
4. The following table shows the probability distribution of a discrete random variable X .
x 5 10 15 20
P( X � x)
0.4 0.4 � r
2
0.19 � r r
(a) Find the value of r .
(b) Find E( X ) .
Another discrete random variable Y is defined such that X �aY
� 20 , a�
given that Var( X ) � 25 and the standard deviation of Y is 1.
�
. It is also
[2]
[2]
(c) Find the value of a .
(d) Find E( Y ) .
[2]
[2]
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