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 

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

 

  1. A

    24

  2. B

    36

  3. C

    6

  4. D

    18

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    Solution:

    We have,

    yi=2xi+3;i=1,2,n Var(Y)=4Var(X) 64=4Var(X)Var(X)=16

    Now,

    zi=32xi;i=1,2,,n Var(Z)=94Var(X)=94×16=36

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