Analysis and Approaches for IBDP Maths Ebook 2 | Page 258

Your Practice Set – Analysis and Approaches for IBDP Mathematics
(c) Find P( X � 0) .
(d) Find P( X � ��
| X � 0) .
(e) Find the value of r if P( X �r) � 0.6 .
[3]
[3]
[3]
3. The random variable X has the probability density function
� 1
�
k sin x 0 � x ��
2
�
f ( x) � � k � � x � � �1.
� 0 otherwise
�
�
(a)
Show that
(b) Find E( X ) .
(c)
(d)
1
k � .
3
Find the exact value of the upper quartile.
Show that
2 2
P
�
�X �
� �
��
� .
� 2�
3
��
� �
(e) Find the exact value of P�
� X � � X � �
2 2
[3]
[3]
[3]
[2]
� � . [3]
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