Analysis and Approaches for IBDP Maths Ebook 1 | Page 256

Your Practice Set – Analysis and Approaches for IBDP Mathematics
83
Paper 1 Section A – Finding unknown
probabilities with given
Example
The random variable X has the following probability distribution.
x 2 4 6
P( X � x)
a b 0.25
Solution
Given that E( X ) � 3.4 , find a .
[6]
P( X � 2) � P( X � 4) � P( X � 6) � 1
(M1) for sum of probabilities
a�b� 0.25 � 1
A1
b�0.75
� a
E( X ) � 3.4
2a� 4 b� (6)(0.25) � 3.4
A1
�2a� 4(0.75 � a) �1.5 � 3.4
(M1) for substitution
�2a
� 4.5 � 3.4
(A1) for simplification
�2a
� � 1.1
a � 0.55
A1 N4
[6]
Exercise 83
1. The random variable X has the following probability distribution.
x 1 2 3 4
P( X � x)
0.2 0.3 a b
Given that E( X ) � 2.62 , find a .
[6]
2. The random variable X has the following probability distribution.
x 20 30 40 50
P( X � x)
0.1 a b 0.1
Given that E( X ) � 33, find the values of a and b .
[7]
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