Answer:
Since
X denotes the sum of the numbers obtained when two fair disc are rolled.
Therefore
X = 2, 3, 4, 5, 6, 76, 8, 9, 10, 11, 12
X
= 2 = {1, 1}
X
= 3 = {(1, 2), (2, 1)}
X
= 4 = {(1, 3), (2, 2), (3, 1)}
X
= 5 = {(1, 4), (2, 3), (3, 2), (4, 1)}
X
= 6 = {(1, 5), (2, 4), (3, 3), (4, 2), (5, 1)}
X
= 7 = {(1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1)}
X
= 8 = {(2, 6), (3, 5), (4, 4), (5, 3), (6, 2)}
X
= 9 = {(3, 6), (4, 5), (5, 4), (6, 3)}
X
= 10 = {(4, 6), (5, 5), (6, 4) }
X
= 11 = {(5, 6), (6, 5)}
X
= 12 = {(6, 6)}.
and
P (X = 12)
We
have
And
Var (X) =
E(X2) ? [E(X)]2
=
54.833 ? 49 = 5.833
and
=
2.415
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