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JEE Main 1-Sep-2021 Shift 2 Solved Paper
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© examsnet.com
Question : 81
Total: 90
Let x be a random variable with distribution.
x
-2
-1
3
4
6
P(X = x)
1
5
a
1
3
1
5
b
If the mean of X is
2.3
and variance of X is
σ
2
, then
100
σ
2
is equal to
[1 Sep 2021 Shift 2]
Your Answer:
Validate
Solution:
Given, mean μ = 2 . 3
⇒
Σ
P
.
x
=
2
.3
⇒
−
2
5
−
a
+
1
+
4
5
+
6
b
=
2
.3
⇒
6
b
−
a
=
0.9
... (i)
Also, ΣP = 1
⇒
1
5
+
a
+
1
3
+
1
5
+
b
=
1
⇒
a
+
b
=
4
15
...(ii)
Solving Eqs. (i) and (ii), we get
a
=
1
10
,
b
=
1
6
Variance
σ
2
=
σ
P
i
x
i
2
−
μ
2
1
5
(
4
)
+
1
10
(
1
)
+
1
3
(
9
)
+
1
5
(
16
)
+
1
6
(
36
)
−
5.29
σ
2
=
7.81
⇒
100
σ
2
=
781
© examsnet.com
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