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UPSC NDA I 2010 Mathematics Paper
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© examsnet.com
Question : 92
Total: 120
The probability distribution of random variable
X
with two missing probabilities
p
1
and
p
2
is given below:
X
P
(
X
)
1
k
2
p
1
3
4
k
4
p
2
5
2
k
It is further given that
P
(
X
≤
2
)
=
0.25
and
P
(
X
≥
4
)
=
0.35
.
Consider the following statements:
I.
p
1
=
p
2
II.
p
1
+
p
2
=
P
(
X
=
3
)
Which of the statements given above is/are correct?
I only
II only
Both I and II
Neither I nor II
Validate
Solution:
Subtracting equation (ii) from equation
(
i
)
Also
k
+
P
1
+
4
k
+
P
2
+
2
k
=
1
7
k
+
P
1
+
P
2
=
1
Adding the equations (iii) and (iv)
4
k
+
P
2
=
0.55
P
2
=
0.55
−
4
k
From (ii)
2
k
+
0.55
−
4
k
=
0.35
k
=
0.10
Now
P
2
=
0.55
−
4
×
.10
P
2
=
0.15
From (i),
P
1
=
0.25
−
k
⇒
P
1
=
0.15
© examsnet.com
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