Analysis and Approaches for IBDP Maths Ebook 1 | Page 258

Your Practice Set – Analysis and Approaches for IBDP Mathematics
84
Paper 1 Section A – Finding
with
given probability distribution
Example
The following table shows the probability distribution of a discrete random variable X .
x 0 2 4 6
P( X � x)
0.4 0.1 2k 3k
(a) Find the value of k .
(b) Find E( X ) .
[3]
[3]
Solution
(a) P( X � 0) � P( X � 2) � P( X � 4) � P( X � 6) � 1 (M1) for sum of probabilities
0.4 � 0.1� 2k� 3k
� 1
5k � 0.5
(A1) for simplification
k � 0.1
A1 N2
[3]
(b) E( X )
� (0)(0.4) � (2)(0.1) � (4)(2 k) � (6)(3 k)
(A1) for correct formula
� (0)(0.4) � (2)(0.1) � (4)(0.2) � (6)(0.3)
(A1) for substitution
� 2.8
A1 N2
[3]
Exercise 84
1. The following table shows the probability distribution of a discrete random variable X .
x 0 1 2 3
P( X � x)
9k k 0.1 0.4
(a) Find the value of k .
(b) Find E( X ) .
[3]
[3]
250
SE Production Limited