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NCERT Class XII Mathematics Chapter - - Solutions

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Question : 65
Total: 101
In a meeting, 70% of the members favour and 30% oppose a certain proposal. A member is selected at random and we take X = 0 if he opposed, and X = 1 if he is in favour. Find E(X) and Var (X).
Solution:  
Random variable X has values 0, 1
X=0⇒P(X)=
30
100
=
3
10

X=1⇒P(X)=
70
100
=
7
10

Thus we have :
 X  0   1  
 P (X)  
3
10
 		 
7
10
 		 
 XP(X)  0  
7
10
   ∑XP(X)=
7
10
  X2   0  1  
  X2P(X)  0  
7
10
   ∑X2P(X)=
7
10
∴E(X)=∑XP(X) =0+
7
10
=
7
10
=0.7
Hence, Var (X) =E(X2)−(E(X))2 =
7
10
−(
7
10
)2=
7
10
−
49
100
 =
21
100
=0.21
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