Analysis and Approaches for IBDP Maths Ebook 2 | Page 257

Exercise 80
1. The random variable X has the probability density function
�
3
�
k( x �1) 1� x �
2
��
2 3
f ( x) � �k( x � 2) � x � 2 .
�� 2
0 otherwise
� �
(a) Find the value of k .
(b) Find E( X ) .
(c)
(d)
[3]
Find the median.
[3]
� 5 �
Find P�X
� �
� 4 � . [3]
[3]
(e)
Find
� 7 5�
P�X
� X � �
� 4 4� . [3]
19
2. The random variable X has the probability density function
� 1 � � � 3� �
�� 2 �x� � � � x� �
�
� � 2 � 2 2
� 1
� �
f ( x) � � cos x � � x � .
� 4 2 2
� 0 otherwise
�
�
(a) Find E( X ) .
(b) Find the variance of X .
[3]
[3]
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