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Q.

If X is a variate taking values x1,x2,…,xn.Y is another variate taking values y1,y2,…,yn such that yi=2xi+3 and σY=8, then the variance of variable Z taking values 32xi;i=1, 2,…,n, is

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a

24

b

36

c

6

d

18

answer is B.

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Detailed Solution

We have,yi=2xi+3;i=1,2,…n∴ Var⁡(Y)=4Var⁡(X)⇒ 64=4Var⁡(X)⇒Var⁡(X)=16Now,zi=32xi;i=1,2,…,n⇒ Var⁡(Z)=94Var⁡(X)=94×16=36
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