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Example Two dice are thrown. Find
the mathematical expression of the sum of the points obtained.
Solution : Let X = sum of points obtained.
Their corresponding probabilities are
P (Xi) = 
Now the expected sum of points is,
E (x) = 
\ E(x) = 7
Example Given the following probability distribution
.
x : 0, 1, 2, 3, 4, 5, 6, 7
Pi : 0, 2l
, 2 l
, l, 3l,
l2, 2 l2 ,
7l2 + l
Find (1) l
(2) Evaluate P (x ³ 5) (3) Evaluate
P (x < 4)
Solution : (1) We know that 
Therefore, 0 + 2l
+ 2l +
l + 3l
+ l2 + 2l2
+ 7l2 + l = 1
10l2
+ 9l - 1 = 0
10l2
+ 10l - l - 1 = 0
l
= 1/10 or l = -1 (discarded)
(2) P (x ³ 5) = P (5)
+ P (6) + P (7)
= l2
+ 2l2 + 7l2
+ l
= 10l2
+ l
= 
(3) P (x < 4) = P
(3) + P (2) + P (1) + P (0)
= l +
2l + 2l
+ 0
= 5l
= 5
= 0.5
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