A random variable X has the following probability distribution:
X
0
1
2
3
4
5
6
7
P(X)
0
k
2k
2k
3k
k 2 2k2 7k2+k
Determine
(i) k
(ii) P(X < 3)
(iii)  P(X > 6)
(iv) P(0 < X < 3)
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PROBABILITY      571
9 The random variable X has a probability distribution P(X) of the following form,
where k is some number :
P(X) =
,
0
2 ,
1
3 ,
2
0, otherwise
k
if x
k if x
k if x
=
⎪⎧
=
⎪⎨
=
⎪
⎪⎩
(a)
Determine the value of k (b)
Find P (X < 2),  P (X ≤ 2), P(X ≥ 2) 10