Question
A person plays a game of throwing an unbiased die under the condition that he could get as many rupees as the number of points
A person plays a game of throwing an unbiased die under the condition that
he could get as many rupees as the number of points obtained on the die. Find the
expectation and variance of his winning. How much should he pay to play in order that
it is a fair game?
Solution:
The probability distribution of the number of rupees won by the person is given
below :
Thus,
E X
Rs
(
)
=
+
+
+
+
+
=
1
1
6
2
1
6
3
1
6
4
1
6
5
1
6
6
1
6
7
2
and
2
1
1
1
1
1
1
91
(
)
1
4
9
16
25
36
6
6
6
6
6
6
6
E X
=
+
+
+
+
+
=
2
2
91
7
35
2.82
6
2
12
=
-
=
=
. Note that the unit of
s
2
will be (Rs)
2
.
X Rs
p X
(
)
(
)
1
2
3
4
5
6
1
6
1
6
1
6
1
6
1
6
1
6
X
1
2
3
p
(
X
)
4
20
12
20
4
20
shouldn't px be 1 2 3 4 5 6
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Probability With Applications and R
Authors: Robert P. Dobrow
1st edition
1118241257, 1118241258, 978-1118241257
