Your Practice Paper – Analysis and Approaches HL for IBDP Mathematics
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Binomial Distribution
� Properties of a random variable X ~ B ( n, p ) following binomial distribution : 1 . Only two outcomes from every independent trial ( Success and failure ) 2 . n : Number of trials 3 . p : Probability of success 4 . X : Number of successes in n trials
� Formulae for binomial distribution :
1 . |
�n� r n�r
P (
X
� r)
�
�
�p
( 1
� p) for 0
�r� n, r �
�r �
|
2 . |
E (
X
)
� np
: Expected value of X
|
3 . Var ( X ) �np( 1 � p) : Variance of X
4 . np( 1 � p)
: Standard deviation of X 5 . P ( X � r) � P ( X � r �1 ) �1� P ( X � r � 1 )
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Continuous Probability Distributions
� 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
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