Analysis and Approaches for IBDP Maths Ebook 2 | Page 259

4. The random variable X has the probability density function
� 1 3
�
x� �3� x�1
20 20
��
1 2 4
f ( x) � �� x � x 1� x � 4 .
�� 15 15
0 otherwise
� �
(a) Find E( X ) .
(b) Find the mode of X .
(c) Find the standard deviation of X .
(d)
Find the value of the 35th percentile.
(e) Find P( X � 2) .
(f) Find P( X �2 | X � 2) .
[3]
[2]
[3]
[3]
[3]
[3]
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