Analysis and Approaches for IBDP Maths Ebook 2 | Page 256

Your Practice Set – Analysis and Approaches for IBDP Mathematics
(b)
(c)
(d)
(e)
1 1
X x x x x x
3 5
2
E( ) � 5 d � ( �5) d
3
3 4 4
� � (A1) for substitution
7 7
E( X ) � �
9 3
(A1) for correct values
28
E( X ) �
9
A1
3
5
3
1 a 1 2 1
d x � ( x �5) dx
�
4 3 4 2
� � A1
3
a
3
� ( x� 5) �
5
3
3
� 1 1 1
�
x
� 4 � � � �
12 �
� � � � 2
� 3 5 � � 1 3 � 2 ��
1
� � � � � ( a �5)
�� � ���
� 4 12 � �12 � 3 ��
2
1 3 1
1 � ( a �5)
� (M1) for valid approach
12 2
3
( a �5) � � 6
3
a �5� � 6
a � 3.182879407
Thus, the median is 3.18.
5 1 2
P( X � 4) � � ( x �5) dx
4
4
(M1) for valid approach
1
P( X �4)
�
12
A1
P( X � 4.5 � X � 4)
P( X � 4.5 | X � 4) �
P( X � 4)
P(4 � X �4.5)
P( X � 4.5 | X � 4) �
P( X � 4)
4.5 1 (
2
x�
5) d
4
A1
A1
� P( X � 4.5 | X � 4) � 4
x
1
A1
12
� 7 �
P( X � 4.5 | X � 4) �12� �
� 96 �
7
P( X � 4.5 | X � 4) � A1
8
(M1) for valid approach
[3]
[4]
[2]
[3]
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