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Question

Consider three finite sets given as
S1={2,5,8,11,up to 100 terms}
S2={1,10,19,28,up to 100 terms}
S3={4,10,16,22,up to 100 terms}

If σ21,σ22 and σ23 are the variance of S1,S2 and S3 respectively, then the value of σ21+σ22σ23σ21 is 


Your Answer
A
3
Correct Answer
B
6
Your Answer
C
8
Your Answer
D
12

Solution

The correct option is B 6
S1={2,5,8,11,up to 100 terms}
S2={1,10,19,28,up to 100 terms}
S3={4,10,16,22,up to 100 terms}

Let nth term of S1 be tn.
Then, nth term of S2 will be 3tn5.
And nth term of S3 will be 2tn

We know that,
Var(aX+b)=a2Var(X)
σ22=(32)σ21=9σ21
and σ23=(22)σ21=4σ21
   
σ21+σ22σ23σ21=σ21+9σ214σ21σ21=6

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