Analysis and Approaches for IBDP Maths Ebook 2 | Page 244

Your Practice Set – Analysis and Approaches for IBDP Mathematics
77
Paper 1 Section A – Linear Transformations of Variables
Example
The following table shows the probability distribution of a discrete random variable X .
x 1 2 3 4
P( X � x)
0.1 r s 0.2
It is given that E( X ) � 2.7 .
(a) Find the value of r and the value of s .
Another discrete random variable Y is defined by Y �5X
� 2. It is also given that the
standard deviation of X is 0.9.
[4]
(b)
Write down the value of
(i) E( Y ) ;
(ii) the standard deviation of Y .
[2]
Solution
(a) P( X �1) � P( X � 2) � P( X � 3) � P( X � 4) � 1 (A1) for correct formula
0.1� r� s�
0.2 � 1
s�0.7
� r
E( X ) � (1)(0.1) � 2r �3 s � (4)(0.2)
�2.7 � 0.1� 2r� 3(0.7 � r) � 0.8
(A1) for substitution
�2.7 � 3�
r
r � 0.3
A1
�s
� 0.7 � 0.3
s � 0.4
A1
(b) (i) 15.5 A1
(ii) 4.5 A1
[4]
[2]
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