Analysis and Approaches for IBDP Maths Ebook 2 | Page 245

Exercise 77
1. The following table shows the probability distribution of a discrete random variable X .
It is given that E( X ) � 2.35 .
x 1 2 5 10
P( X � x)
r� s r� s 0.15 0.05
(a) Find the value of r and the value of s .
Another discrete random variable Y is defined by Y �� X
Var( X ) � 4.9275 .
. It is also given that
[4]
(b)
Write down the value of
(i) E( Y ) ;
(ii) Var( Y ) .
[2]
18
2. The following table shows the probability distribution of a discrete random variable X .
It is given that E( X ) � 24 .
x 10 20 t 2t
P( X � x)
0.2 0.5 r
2
r � 0.06
(a) Find the value of r and the value of t .
[4]
Another discrete random variable Y is defined by Y � �4X
� 3. It is also given that the
standard deviation of X is 184 .
(b) If the standard deviation of Y is q 46
�
, q� , find the value of q .
[2]
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