Analysis and Approaches for IBDP Maths Ebook 2 | Page 250

Your Practice Set – Analysis and Approaches for IBDP Mathematics
Chapter
19
Continuous Probability
Distributions
SUMMARY POINTs
� Properties of a continuous random variable X :
b
1. � f ( x )d x � 1
a
�
b
� f ( x)
a � x �b
px ( ) � �
� 0 otherwise
2. E( X ) � x�
f ( x)dx
: Expected value of X
a
3. Q
2
: Median of X , which is the solution of the equation
4. Q
1
: Lower quartile of X , which is the solution of
5. Q
3
: Upper quartile of X , which is the solution of
6. The maximum value of f( x ) is the mode of X
7.
2 2
E( ) ��
b
� ( )d
a
X x f x x
�
Q1
a
�
Q3
a
�
Q2
a
f ( x)dx � 0.5
f ( x)dx � 0.25
f ( x)dx � 0.75
Solutions of Chapter 19
240
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