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MHT CET 2016 Math Solved Paper
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© examsnet.com
Question : 1
Total: 50
Let X ~ B (n, p), if E(X) = 5, Var (X) = 2.5, then p(X < 1) is equal to
(
1
2
)
11
(
1
2
)
10
(
1
2
)
6
(
1
2
)
91
Validate
Solution:
(b) Here, mean E(X) = 5
and variance, Var (X) = 2.5
⇒ np = 5 and npq = 2.5
⇒ 5q = 2.5 ⇒ q =
1
2
Also,p + q = l ⇒ P = 1 -
1
2
=
1
2
∵ np = 5
⇒ n ×
1
2
= 5 ⇒ n = 10
p
(
X
<
1
)
=
p
(
X
=
0
)
=
n
C
r
p
r
q
n
−
r
=
10
C
0
(
1
2
)
0
(
/
1
2
)
10
−
0
=
1
×
1
×
(
1
2
)
10
=
(
1
2
)
10
© examsnet.com
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