Analysis and Approaches for IBDP Maths Ebook 2 | Page 248

Your Practice Set – Analysis and Approaches for IBDP Mathematics
Exercise 78
1. The following table shows the probability distribution of a discrete random variable X .
x 18 24 33 39
P( X � x)
0.343 0.189 0.0265 0.4415
(a) Find E( X ) .
(b)
Find
2
E( X ) .
(c) Hence, find the standard deviation of X .
[2]
[2]
[2]
2. The following table shows the probability distribution of a discrete random variable X .
x 4 9 16 25
P( X � x)
0.45 0.2 0.2 0.15
(a) Find E( X ) .
Another discrete random variable Y is defined such that
are negative.
X
� Y
2
, where all values of y
[2]
(b) Find E( Y ) .
(c) Hence, find the standard deviation of Y .
[2]
[2]
3. The probability distribution of a discrete random variable X is defined by
x
P( X � x)
� , x � 1, 2, 3, 4, 5, 6.
42k
(a) Find the value of k .
(b) Find E( X ) .
(c) Hence, find Var( X ) .
[2]
[2]
[3]
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