Analysis and Approaches for IBDP Maths Ebook 2 | Page 243

Chapter
18
Discrete Probability
Distributions
18
SUMMARY POINTs
� Properties of a discrete random variable X :
X x
1
x
2
… x
n
P( X x)
� P( X � x1
) X x2
P( � ) … P( X � x n
)
E( X ) � x P( X � x ) � x P( X � x ) � � x P( X � x ): Expected value of X
1.
1 1 2 2
2.
3.
E( X ) � x P( X � x ) � x P( X � x ) � � x P( X � x )
2 2 2 2
1 1 2 2
n
Var( X ) E( X ) (E( X ))
2 2
� � : Variance of X
n
n
n
� Linear transformation of a random variable X :
1. E( aX �b) � aE( X ) � b : Expected value of X
2.
2
Var( aX �b) � a Var( X )
Solutions of Chapter 18
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