Analysis and Approaches for IBDP Maths Ebook 2 | Page 255

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Paper 2 Section B – Problems Involving Probability
Example
The random variable X has the probability density function
� 5
�
k � x�3
3
�
2
f ( x) � �k( x � 5) 3 � x � 5 .
�� 0 otherwise
�
(a) Find the value of k .
(b) Find E( X ) .
(c)
Find the median.
(d) Find P( X � 4) .
(e) Find P( X �4.5 | X � 4) .
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Solution
(a)
3 k 5
2
5 d x � k ( x �5) d x �1
3
3
� � (M1) for valid approach
�
kx
5
3 �k
3�
5
�
x
3 3 �
� �3
�
� ( � 5) �1
A1
� 5k
� � � 8k
��
�3k
� � � �0 �� � ���1
� 3 � � � 3 ��
4k � 1
1
k � A1
4
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