Analysis and Approaches for IBDP Maths Ebook 2 | Page 247

78
Paper 2 Section A – Variance of Random Variables
Example
The following table shows the probability distribution of a discrete random variable X .
x 4 6 9 10
P( X � x)
15
28
5
28
1
56
15
56
(a) Find E( X ) .
(b)
Solution
Find
2
E( X ) .
(c) Hence, find Var( X ) .
[2]
[2]
[2]
18
(a)
(b)
(c)
� 15 � � 5 � � 1 � � 15 �
E( X ) � (4) � � � (6) � � � (9) � � � (10) � �
� 28 � � 28 � � 56 � � 56 �
(A1) for correct formula
339
E( X ) �
56
A1
2 2 � 15 � 2 � 5 �
E( X ) �(4 ) � � �(6 ) � �
� 28 � � 28 �
2 � 1 � 2 � 15 �
�(9 ) � � �(10 ) � �
� 56 � � 56 �
(A1) for correct formula
2 2421
E( X ) �
56
A1
Var( X ) E( X ) E( X )
2 2
� � (A1) for correct formula
2421 �339
�
Var( X ) � � � �
56 � 56 �
Var( X ) � 6.586415816
2
Var( X ) � 6.59
A1
[2]
[2]
[2]
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